{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Schwarzschild spacetime\n", "\n", "This worksheet illustrates a few capabilities of SageMath in computations regarding Schwarzschild spacetime. The corresponding tools have been developed within the [SageManifolds](http://sagemanifolds.obspm.fr) project (version 1.2, as included in SageMath 8.2).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.2/SM_Schwarzschild.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 8.2 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.2, Release Date: 2018-05-05'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX rendering:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime manifold\n", "\n", "We declare the Schwarzschild spacetime as a 4-dimensional Lorentzian manifold:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4-dimensional Lorentzian manifold M" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = Manifold(4, 'M', r'\\mathcal{M}', structure='Lorentzian')\n", "M" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
The spacetime manifold $\\mathcal{M}$ can be split into 4 regions, corresponding to the 4 quadrants in the Kruskal diagram.Let us denote by $\\mathcal{R}_{\\mathrm{I}}$ to $\\mathcal{R}_{\\mathrm{IV}}$ the interiors of these 4 regions. $\\mathcal{R}_{\\mathrm{I}}$ and $\\mathcal{R}_{\\mathrm{III}}$ are asymtotically flat regions outside the event horizon; $\\mathcal{R}_{\\mathrm{II}}$ is inside the future event horizon and $\\mathcal{R}_{\\mathrm{IV}}$ is inside the past event horizon.
" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(Open subset R_I of the 4-dimensional Lorentzian manifold M,\n", " Open subset R_II of the 4-dimensional Lorentzian manifold M,\n", " Open subset R_III of the 4-dimensional Lorentzian manifold M,\n", " Open subset R_IV of the 4-dimensional Lorentzian manifold M)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "regI = M.open_subset('R_I', r'\\mathcal{R}_{\\mathrm{I}}')\n", "regII = M.open_subset('R_II', r'\\mathcal{R}_{\\mathrm{II}}')\n", "regIII = M.open_subset('R_III', r'\\mathcal{R}_{\\mathrm{III}}')\n", "regIV = M.open_subset('R_IV', r'\\mathcal{R}_{\\mathrm{IV}}')\n", "regI, regII, regIII, regIV" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameter $m$ of the Schwarzschild spacetime is declared as a symbolic variable:
" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "m = var('m') ; assume(m>=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The standard Boyer-Lindquist coordinates (also called Schwarzschild coordinates) are defined on $\\mathcal{R}_{\\mathrm{I}}\\cup \\mathcal{R}_{\\mathrm{II}}$
" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset R_I_union_R_II of the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "regI_II = regI.union(regII) ; regI_II" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (R_I_union_R_II, (t, r, th, ph))\n" ] } ], "source": [ "X.We naturally introduce two subcharts as the restrictions of the chart $X$ to regions $\\mathcal{R}_{\\mathrm{I}}$ and $\\mathcal{R}_{\\mathrm{II}}$ respectively. Since, in terms of the Boyer-Lindquist coordinates, $\\mathcal{R}_{\\mathrm{I}}$ (resp. $\\mathcal{R}_{\\mathrm{II}}$) is defined by $r>2m$ (resp. $r<2m$), we set
" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I, (t, r, th, ph))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_I = X.restrict(regI, r>2*m) ; X_I" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_II, (t, r, th, ph))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_II = X.restrict(regII, r<2*m) ; X_II" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this stage, the manifold's atlas has 3 charts:
" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (R_I_union_R_II, (t, r, th, ph)),\n", " Chart (R_I, (t, r, th, ph)),\n", " Chart (R_II, (t, r, th, ph))]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.atlas()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I_union_R_II, (t, r, th, ph))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.default_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Three vector frames have been defined on the manifold: the three coordinate frames:
" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dt,d/dr,d/dth,d/dph))]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.frames()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph))\n" ] } ], "source": [ "print(M.default_frame())" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset R_I_union_R_II of the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.default_frame().domain()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metric tensor\n", "\n", "The metric tensor is obtained as follows:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lorentzian metric g on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "g = M.metric()\n", "print(g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One has to set its components in the coordinate frame associated with Schwarzschild coordinates, which is the current manifold's default frame:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "g[0,0], g[1,1] = -(1-2*m/r), 1/(1-2*m/r)\n", "g[2,2], g[3,3] = r^2, (r*sin(th))^2" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = (2*m/r - 1) dt*dt - 1/(2*m/r - 1) dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, let us consider a vector field defined only on $\\mathcal{R}_{\\mathrm{I}}$:
" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dt + (-2*m/r + 1) d/dr" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = regI.vector_field('v')\n", "v[0] = 1\n", "v[1] = 1 - 2*m/r\n", "# unset components are zero \n", "v.display()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset R_I of the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.domain()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4-dimensional Lorentzian manifold M" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.domain()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since $\\mathcal{R}_{\\mathrm{I}}\\subset \\mathcal{M}$, it is possible to apply $g$ to $v$:
" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field g(v,v) on the Open subset R_I of the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "s = g(v,v) ; print(s)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g(v,v): R_I --> R\n", " (t, r, th, ph) |--> 0" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.display() # v is indeed a null vector" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Levi-Civita connection $\\nabla$ associated with $g$:
\n", "Let us verify that the covariant derivative of $g$ with respect to $\\nabla$ vanishes identically:
" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g) == 0" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The nonzero Christoffel symbols of $g$ with respect to Schwarzschild coordinates, skipping those that can be deduced by symmetry:
" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Gam^t_t,r = -m/(2*m*r - r^2) \n", "Gam^r_t,t = -(2*m^2 - m*r)/r^3 \n", "Gam^r_r,r = m/(2*m*r - r^2) \n", "Gam^r_th,th = 2*m - r \n", "Gam^r_ph,ph = (2*m - r)*sin(th)^2 \n", "Gam^th_r,th = 1/r \n", "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_r,ph = 1/r \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann curvature tensor associated with $g$:
" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "R = g.riemann() ; print(R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Weyl conformal tensor associated with $g$:
" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field C(g) of type (1,3) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "C = g.weyl() ; print(C)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "C(g) = -2*m/(2*m*r^2 - r^3) d/dt*dr*dt*dr + 2*m/(2*m*r^2 - r^3) d/dt*dr*dr*dt - m/r d/dt*dth*dt*dth + m/r d/dt*dth*dth*dt - m*sin(th)^2/r d/dt*dph*dt*dph + m*sin(th)^2/r d/dt*dph*dph*dt - 2*(2*m^2 - m*r)/r^4 d/dr*dt*dt*dr + 2*(2*m^2 - m*r)/r^4 d/dr*dt*dr*dt - m/r d/dr*dth*dr*dth + m/r d/dr*dth*dth*dr - m*sin(th)^2/r d/dr*dph*dr*dph + m*sin(th)^2/r d/dr*dph*dph*dr + (2*m^2 - m*r)/r^4 d/dth*dt*dt*dth - (2*m^2 - m*r)/r^4 d/dth*dt*dth*dt - m/(2*m*r^2 - r^3) d/dth*dr*dr*dth + m/(2*m*r^2 - r^3) d/dth*dr*dth*dr + 2*m*sin(th)^2/r d/dth*dph*dth*dph - 2*m*sin(th)^2/r d/dth*dph*dph*dth + (2*m^2 - m*r)/r^4 d/dph*dt*dt*dph - (2*m^2 - m*r)/r^4 d/dph*dt*dph*dt - m/(2*m*r^2 - r^3) d/dph*dr*dr*dph + m/(2*m*r^2 - r^3) d/dph*dr*dph*dr - 2*m/r d/dph*dth*dth*dph + 2*m/r d/dph*dth*dph*dth" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Ricci tensor associated with $g$:
" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms Ric(g) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "Ric = g.ricci() ; print(Ric)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that the Schwarzschild metric is a solution of the vacuum Einstein equation:
" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric == 0" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Ric(g) = 0" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric.display() # another view of the above" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Contrary to the Ricci tensor, the Riemann tensor does not vanish:
" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],\n", " [[0, -2*m/(2*m*r^2 - r^3), 0, 0],\n", " [2*m/(2*m*r^2 - r^3), 0, 0, 0],\n", " [0, 0, 0, 0],\n", " [0, 0, 0, 0]],\n", " [[0, 0, -m/r, 0], [0, 0, 0, 0], [m/r, 0, 0, 0], [0, 0, 0, 0]],\n", " [[0, 0, 0, -m*sin(th)^2/r],\n", " [0, 0, 0, 0],\n", " [0, 0, 0, 0],\n", " [m*sin(th)^2/r, 0, 0, 0]]],\n", " [[[0, -2*(2*m^2 - m*r)/r^4, 0, 0],\n", " [2*(2*m^2 - m*r)/r^4, 0, 0, 0],\n", " [0, 0, 0, 0],\n", " [0, 0, 0, 0]],\n", " [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],\n", " [[0, 0, 0, 0], [0, 0, -m/r, 0], [0, m/r, 0, 0], [0, 0, 0, 0]],\n", " [[0, 0, 0, 0],\n", " [0, 0, 0, -m*sin(th)^2/r],\n", " [0, 0, 0, 0],\n", " [0, m*sin(th)^2/r, 0, 0]]],\n", " [[[0, 0, (2*m^2 - m*r)/r^4, 0],\n", " [0, 0, 0, 0],\n", " [-(2*m^2 - m*r)/r^4, 0, 0, 0],\n", " [0, 0, 0, 0]],\n", " [[0, 0, 0, 0],\n", " [0, 0, -m/(2*m*r^2 - r^3), 0],\n", " [0, m/(2*m*r^2 - r^3), 0, 0],\n", " [0, 0, 0, 0]],\n", " [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],\n", " [[0, 0, 0, 0],\n", " [0, 0, 0, 0],\n", " [0, 0, 0, 2*m*sin(th)^2/r],\n", " [0, 0, -2*m*sin(th)^2/r, 0]]],\n", " [[[0, 0, 0, (2*m^2 - m*r)/r^4],\n", " [0, 0, 0, 0],\n", " [0, 0, 0, 0],\n", " [-(2*m^2 - m*r)/r^4, 0, 0, 0]],\n", " [[0, 0, 0, 0],\n", " [0, 0, 0, -m/(2*m*r^2 - r^3)],\n", " [0, 0, 0, 0],\n", " [0, m/(2*m*r^2 - r^3), 0, 0]],\n", " [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2*m/r], [0, 0, 2*m/r, 0]],\n", " [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]]]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R[:]" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g) = -2*m/(2*m*r^2 - r^3) d/dt*dr*dt*dr + 2*m/(2*m*r^2 - r^3) d/dt*dr*dr*dt - m/r d/dt*dth*dt*dth + m/r d/dt*dth*dth*dt - m*sin(th)^2/r d/dt*dph*dt*dph + m*sin(th)^2/r d/dt*dph*dph*dt - 2*(2*m^2 - m*r)/r^4 d/dr*dt*dt*dr + 2*(2*m^2 - m*r)/r^4 d/dr*dt*dr*dt - m/r d/dr*dth*dr*dth + m/r d/dr*dth*dth*dr - m*sin(th)^2/r d/dr*dph*dr*dph + m*sin(th)^2/r d/dr*dph*dph*dr + (2*m^2 - m*r)/r^4 d/dth*dt*dt*dth - (2*m^2 - m*r)/r^4 d/dth*dt*dth*dt - m/(2*m*r^2 - r^3) d/dth*dr*dr*dth + m/(2*m*r^2 - r^3) d/dth*dr*dth*dr + 2*m*sin(th)^2/r d/dth*dph*dth*dph - 2*m*sin(th)^2/r d/dth*dph*dph*dth + (2*m^2 - m*r)/r^4 d/dph*dt*dt*dph - (2*m^2 - m*r)/r^4 d/dph*dt*dph*dt - m/(2*m*r^2 - r^3) d/dph*dr*dr*dph + m/(2*m*r^2 - r^3) d/dph*dr*dph*dr - 2*m/r d/dph*dth*dth*dph + 2*m/r d/dph*dth*dph*dth" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The nonzero components of the Riemann tensor, skipping those that can be deduced by antisymmetry:
" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g)^t_r,t,r = -2*m/(2*m*r^2 - r^3) \n", "Riem(g)^t_th,t,th = -m/r \n", "Riem(g)^t_ph,t,ph = -m*sin(th)^2/r \n", "Riem(g)^r_t,t,r = -2*(2*m^2 - m*r)/r^4 \n", "Riem(g)^r_th,r,th = -m/r \n", "Riem(g)^r_ph,r,ph = -m*sin(th)^2/r \n", "Riem(g)^th_t,t,th = (2*m^2 - m*r)/r^4 \n", "Riem(g)^th_r,r,th = -m/(2*m*r^2 - r^3) \n", "Riem(g)^th_ph,th,ph = 2*m*sin(th)^2/r \n", "Riem(g)^ph_t,t,ph = (2*m^2 - m*r)/r^4 \n", "Riem(g)^ph_r,r,ph = -m/(2*m*r^2 - r^3) \n", "Riem(g)^ph_th,th,ph = -2*m/r " ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.display_comp(only_nonredundant=True)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[0 0 0 0]\n", "[0 0 0 0]\n", "[0 0 0 0]\n", "[0 0 0 0]" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the Ricci tensor is zero, the Weyl tensor is of course equal to the Riemann tensor:
" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C == R" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check the Bianchi identity $\\nabla_p R^i_{\\ \\, j kl} + \\nabla_k R^i_{\\ \\, jlp} + \\nabla_l R^i_{\\ \\, jpk} = 0$:
" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(Riem(g)) of type (1,4) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "DR = nab(R) ; print(DR)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n" ] } ], "source": [ "for i in M.irange():\n", " for j in M.irange():\n", " for k in M.irange():\n", " for l in M.irange():\n", " for p in M.irange():\n", " print DR[i,j,k,l,p] + DR[i,j,l,p,k] + DR[i,j,p,k,l] ," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that if we turn the first $+$ sign into a $-$ one, the Bianchi identity does no longer hold:
" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -12*m/(2*m*r^3 - r^4) 0 0 12*m/(2*m*r^3 - r^4) 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m/r^2 0 0 0 0 0 6*m/r^2 0 0 0 0 0 0 0 0 0 0 -6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m/r^2 0 0 0 0 0 6*m/r^2 0 0 0 0 0 0 0 0 -6*m/r^2 0 0 6*m/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m*sin(th)^2/r^2 0 0 6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -12*(2*m^2 - m*r)/r^5 0 0 12*(2*m^2 - m*r)/r^5 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*(4*m^3 - 4*m^2*r + m*r^2)/r^4 0 0 0 0 0 6*(4*m^3 - 4*m^2*r + m*r^2)/r^4 0 0 0 0 0 0 0 0 0 0 -6*(4*m^3 - 4*m^2*r + m*r^2)*sin(th)^2/r^4 0 0 0 0 0 0 0 0 6*(4*m^3 - 4*m^2*r + m*r^2)*sin(th)^2/r^4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m/r^2 0 0 6*m/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6*(2*m^2 - m*r)*sin(th)^2/r 0 0 -6*(2*m^2 - m*r)*sin(th)^2/r 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m*sin(th)^2/r^2 0 0 0 0 0 6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*(2*m^2 - m*r)*sin(th)^2/r 0 0 6*(2*m^2 - m*r)*sin(th)^2/r 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6*(2*m^2 - m*r)/r^5 0 0 0 0 0 -6*(2*m^2 - m*r)/r^5 0 0 0 0 0 0 0 0 6*(2*m^2 - m*r)/r^5 0 0 -6*(2*m^2 - m*r)/r^5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m/(2*m*r^3 - r^4) 0 0 6*m/(2*m*r^3 - r^4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6*m*sin(th)^2/r^2 0 0 -6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12*m*sin(th)^2/r^2 0 0 -12*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 6*m*sin(th)^2/r^2 0 0 0 0 0 -6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 -6*m*sin(th)^2/r^2 0 0 6*m*sin(th)^2/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6*(2*m^2 - m*r)/r^5 0 0 0 0 0 0 0 0 -6*(2*m^2 - m*r)/r^5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6*(2*m^2 - m*r)/r^5 0 0 -6*(2*m^2 - m*r)/r^5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m/(2*m*r^3 - r^4) 0 0 0 0 0 6*m/(2*m*r^3 - r^4) 0 0 0 0 0 0 0 0 0 0 0 0 0 -6*m/r^2 0 0 6*m/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -12*m/r^2 0 0 12*m/r^2 0 0 0 0 0 0 0 0 -6*m/r^2 0 0 0 0 0 6*m/r^2 0 0 0 0 0 0 0 0 6*m/r^2 0 0 -6*m/r^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n" ] } ], "source": [ "for i in M.irange():\n", " for j in M.irange():\n", " for k in M.irange():\n", " for l in M.irange():\n", " for p in M.irange():\n", " print DR[i,j,k,l,p] - DR[i,j,l,p,k] + DR[i,j,p,k,l] ," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first introduce tensor $R^\\flat$, of components $R_{ijkl} = g_{ip} R^p_{\\ \\, jkl}$:
" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,4) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "dR = R.down(g) ; print(dR)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and tensor $R^\\sharp$, of components $R^{ijkl} = g^{jp} g^{kq} g^{lr} R^i_{\\ \\, pqr}$:
" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (4,0) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "uR = R.up(g) ; print(uR)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kretschmann scalar is $K := R^{ijkl} R_{ijkl}$:
" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "48*m^2/r^6" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Kr = 0\n", "for i in M.irange():\n", " for j in M.irange():\n", " for k in M.irange():\n", " for l in M.irange():\n", " Kr += uR[i,j,k,l]*dR[i,j,k,l]\n", "Kr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of the above loops, the Kretschmann scalar can also be computed by means of the contract() method, asking that the contraction takes place on all indices (positions 0, 1, 2, 3):
" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "48*m^2/r^6" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Kr = uR.contract(0, 1, 2, 3, dR, 0, 1, 2, 3)\n", "Kr.expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The contraction can also be performed by means of index notations:
" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "48*m^2/r^6" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Kr = uR['^{ijkl}']*dR['_{ijkl}']\n", "Kr.expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us introduce new coordinates on the spacetime manifold: the ingoing Eddington-Finkelstein ones:
" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (R_I_union_R_II, (v, r, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I_union_R_II, (v, r, th, ph))" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_EF.The change from Schwarzschild (Boyer-Lindquist) coordinates to the ingoing Eddington-Finkelstein ones:
" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "ch_BL_EF_I = X_I.transition_map(X_EF, [t+r+2*m*ln(r/(2*m)-1), r, th, ph], restrictions2=r>2*m)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_I, (t, r, th, ph)) to Chart (R_I, (v, r, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Change of coordinates from Chart (R_I, (t, r, th, ph)) to Chart (R_I, (v, r, th, ph))" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(ch_BL_EF_I) ; ch_BL_EF_I" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = 2*m*log(1/2*r/m - 1) + r + t\n", "r = r\n", "th = th\n", "ph = ph" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_BL_EF_I.display()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I, (v, r, th, ph))" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_EF_I = X_EF.restrict(regI) ; X_EF_I" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "ch_BL_EF_II = X_II.transition_map(X_EF, [t+r+2*m*ln(1-r/(2*m)), r, th, ph], restrictions2=r<2*m)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_II, (t, r, th, ph)) to Chart (R_II, (v, r, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Change of coordinates from Chart (R_II, (t, r, th, ph)) to Chart (R_II, (v, r, th, ph))" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(ch_BL_EF_II) ; ch_BL_EF_II" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = 2*m*log(-1/2*r/m + 1) + r + t\n", "r = r\n", "th = th\n", "ph = ph" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_BL_EF_II.display()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_II, (v, r, th, ph))" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_EF_II = X_EF.restrict(regII) ; X_EF_II" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The manifold's atlas has now 6 charts:
" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (R_I_union_R_II, (t, r, th, ph)),\n", " Chart (R_I, (t, r, th, ph)),\n", " Chart (R_II, (t, r, th, ph)),\n", " Chart (R_I_union_R_II, (v, r, th, ph)),\n", " Chart (R_I, (v, r, th, ph)),\n", " Chart (R_II, (v, r, th, ph))]" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default chart is 'BL':
" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I_union_R_II, (t, r, th, ph))" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.default_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The change from Eddington-Finkelstein coordinates to the Schwarzschild (Boyer-Lindquist) ones, computed as the inverse of ch_BL_EF:
" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_I, (v, r, th, ph)) to Chart (R_I, (t, r, th, ph))\n" ] } ], "source": [ "ch_EF_BL_I = ch_BL_EF_I.inverse() ; print(ch_EF_BL_I)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = -2*m*log(1/2*r/m - 1) - r + v\n", "r = r\n", "th = th\n", "ph = ph" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_EF_BL_I.display()" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_II, (v, r, th, ph)) to Chart (R_II, (t, r, th, ph))\n" ] } ], "source": [ "ch_EF_BL_II = ch_BL_EF_II.inverse() ; print(ch_EF_BL_II)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = -2*m*log(-1/2*r/m + 1) - r + v\n", "r = r\n", "th = th\n", "ph = ph" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_EF_BL_II.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this stage, 6 vector frames have been defined on the manifold: the 6 coordinate frames associated with the various charts:
" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I_union_R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dv,d/dr,d/dth,d/dph))]" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default frame is:
" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph))" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coframes are the duals of the defined vector frames:
" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate coframe (R_I_union_R_II, (dt,dr,dth,dph)),\n", " Coordinate coframe (R_I, (dt,dr,dth,dph)),\n", " Coordinate coframe (R_II, (dt,dr,dth,dph)),\n", " Coordinate coframe (R_I_union_R_II, (dv,dr,dth,dph)),\n", " Coordinate coframe (R_I, (dv,dr,dth,dph)),\n", " Coordinate coframe (R_II, (dv,dr,dth,dph))]" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.coframes()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If not specified, tensor components are assumed to refer to the manifold's default frame. For instance, for the metric tensor:
" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = (2*m/r - 1) dt*dt - 1/(2*m/r - 1) dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ 2*m/r - 1 0 0 0]\n", "[ 0 -1/(2*m/r - 1) 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The tensor components in the frame associated with Eddington-Finkelstein coordinates in Region I are obtained by providing the frame to the function display():
" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = (2*m - r)/r dv*dv + dv*dr + dr*dv + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_EF_I.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are also returned by the method comp(), with the frame as argument:
" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ (2*m - r)/r 1 0 0]\n", "[ 1 0 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.comp(X_EF_I.frame())[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or, as a schortcut,
" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ (2*m - r)/r 1 0 0]\n", "[ 1 0 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[X_EF_I.frame(),:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the metric components in the frame associated with Eddington-Finkelstein coordinates in Region II are obtained by
Note that their form is identical to that in Region I.
\n", "\n", "Let us perform the plot in Region I:
" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_I.plot(X_EF_I, ranges={t:(0,8), r:(2.1,10)}, fixed_coords={th:pi/2,ph:0}, ambient_coords=(r,v), style={t:'--', r:'-'}, parameters={m:1})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us introduce the orthonormal tetrad $(e_\\alpha)$ associated with the static observers in Schwarzschild spacetime, i.e. the observers whose worldlines are parallel to the timelike Killing vector in the Region I.
\n", "The orthonormal tetrad is defined via a tangent-space automorphism that relates it to the Boyer-Lindquist coordinate frame in Region I:
" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[1/sqrt(-2*m/r + 1) 0 0 0]\n", "[ 0 sqrt(-2*m/r + 1) 0 0]\n", "[ 0 0 1/r 0]\n", "[ 0 0 0 1/(r*sin(th))]" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_to_stat = regI.automorphism_field()\n", "ch_to_stat[0,0], ch_to_stat[1,1] = 1/sqrt(1-2*m/r), sqrt(1-2*m/r)\n", "ch_to_stat[2,2], ch_to_stat[3,3] = 1/r, 1/(r*sin(th))\n", "ch_to_stat[:]" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector frame (R_I, (e_0,e_1,e_2,e_3))\n" ] } ], "source": [ "e = X_I.frame().new_frame(ch_to_stat, 'e') ; print(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this stage, 7 vector frames have been defined on the manifold $\\mathcal{M}$:
" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I_union_R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Vector frame (R_I, (e_0,e_1,e_2,e_3))]" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first vector of the tetrad is the static observer 4-velocity:
" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field e_0 on the Open subset R_I of the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "print(e[0])" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_0 = 1/sqrt(-2*m/r + 1) d/dt" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[0].display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As any 4-velocity, it is a unit timelike vector:
" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-1" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[0],e[0]).expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Equivalently, we may use the method `dot` to get the scalar product (since $g$ is the default metric on $\\mathcal{M}$):" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-1" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[0].dot(e[0]).expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that the tetrad $(e_\\alpha)$ is orthonormal:
" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1 0 0 0 \n", "0 1 0 0 \n", "0 0 1 0 \n", "0 0 0 1 \n" ] } ], "source": [ "for i in M.irange():\n", " for j in M.irange():\n", " print e[i].dot(e[j]).expr() , \n", " print \" \"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another view of the above result:
" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[-1 0 0 0]\n", "[ 0 1 0 0]\n", "[ 0 0 1 0]\n", "[ 0 0 0 1]" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or, equivalently,
" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -e^0*e^0 + e^1*e^1 + e^2*e^2 + e^3*e^3" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the 4-velocity $e_0$ and the vector $e_1$ in terms of the frame associated with Eddington-Finkelstein coordinates:
" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_0 = sqrt(r)/sqrt(-2*m + r) d/dv" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[0].display(X_EF_I.frame())" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_1 = sqrt(r)/sqrt(-2*m + r) d/dv + sqrt(-2*m + r)/sqrt(r) d/dr" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display(X_EF_I.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Contrary to vectors of a coordinate frame, the vectors of the tetrad $e$ do not commute: their structure coefficients are not identically zero:
" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, -m*sqrt(-2*m + r)/((2*m*r - r^2)*sqrt(r)), 0, 0],\n", " [m*sqrt(-2*m + r)/((2*m*r - r^2)*sqrt(r)), 0, 0, 0],\n", " [0, 0, 0, 0],\n", " [0, 0, 0, 0]],\n", " [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],\n", " [[0, 0, 0, 0],\n", " [0, 0, -sqrt(-2*m + r)/r^(3/2), 0],\n", " [0, sqrt(-2*m + r)/r^(3/2), 0, 0],\n", " [0, 0, 0, 0]],\n", " [[0, 0, 0, 0],\n", " [0, 0, 0, -sqrt(-2*m + r)/r^(3/2)],\n", " [0, 0, 0, -cos(th)/(r*sin(th))],\n", " [0, sqrt(-2*m + r)/r^(3/2), cos(th)/(r*sin(th)), 0]]]" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coeff()[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Equivalently, the Lie derivative of one vector along another one is not necessarily zero:
" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "m*sqrt(-2*m + r)/((2*m*r - r^2)*sqrt(r)) e_0" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[0].lie_der(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The curvature 2-form $\\Omega^0_{\\ \\, 1}$ associated with the tetrad $(e_\\alpha)$:
" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "curvature (0,1) of connection nabla_g w.r.t. Vector frame (R_I, (e_0,e_1,e_2,e_3)) = 2*m/r^3 dt/\\dr" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.connection().curvature_form(0,1,e).display(X_I.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now introduce the Kruskal-Szekeres coordinates $(U,V,\\theta,\\varphi)$ on the spacetime manifold, via the standard transformation expressing them in terms of the Boyer-Lindquist coordinates $(t,r,\\theta,\\varphi)$:
" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset R_I_union_R_II_union_R_III_union_R_IV of the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M0 = regI.union(regII).union(regIII).union(regIV) ; M0" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I_union_R_II_union_R_III_union_R_IV, (U, V, th, ph))" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_KS. = M0.chart(r'U V th:(0,pi):\\theta ph:(0,2*pi):\\varphi')\n", "X_KS.add_restrictions(V^2 < 1 + U^2)\n", "X_KS" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I, (U, V, th, ph))" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_KS_I = X_KS.restrict(regI, [U>0, V-U]) ; X_KS_I" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_I, (t, r, th, ph)) to Chart (R_I, (U, V, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "U = sqrt(1/2*r/m - 1)*cosh(1/4*t/m)*e^(1/4*r/m)\n", "V = sqrt(1/2*r/m - 1)*e^(1/4*r/m)*sinh(1/4*t/m)\n", "th = th\n", "ph = ph" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_BL_KS_I = X_I.transition_map(X_KS_I, [sqrt(r/(2*m)-1)*exp(r/(4*m))*cosh(t/(4*m)), \n", " sqrt(r/(2*m)-1)*exp(r/(4*m))*sinh(t/(4*m)), th, ph])\n", "print(ch_BL_KS_I)\n", "ch_BL_KS_I.display()" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_II, (U, V, th, ph))" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_KS_II = X_KS.restrict(regII, [V>0, V>U, V>-U]) ; X_KS_II" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_II, (t, r, th, ph)) to Chart (R_II, (U, V, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "U = sqrt(-1/2*r/m + 1)*e^(1/4*r/m)*sinh(1/4*t/m)\n", "V = sqrt(-1/2*r/m + 1)*cosh(1/4*t/m)*e^(1/4*r/m)\n", "th = th\n", "ph = ph" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_BL_KS_II = X_II.transition_map(X_KS_II, [sqrt(1-r/(2*m))*exp(r/(4*m))*sinh(t/(4*m)), \n", " sqrt(1-r/(2*m))*exp(r/(4*m))*cosh(t/(4*m)), th, ph])\n", "print(ch_BL_KS_II)\n", "ch_BL_KS_II.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We draw the Boyer-Lindquist chart in Region I (red) and Region II (green), with lines of constant $r$ being dashed:
" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 52 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphI = X_I.plot(X_KS, ranges={t:(-12,12), r:(2.001,5)}, number_values={t:17, r:9}, \n", " fixed_coords={th:pi/2,ph:0}, ambient_coords=(U,V), \n", " style={t:'--', r:'-'}, parameters={m:1})\n", "graphII = X_II.plot(X_KS, ranges={t:(-12,12), r:(0.001,1.999)}, number_values={t:17, r:9}, \n", " fixed_coords={th:pi/2,ph:0}, ambient_coords=(U,V), \n", " style={t:'--', r:'-'}, color='green', parameters={m:1})\n", "show(graphI+graphII, xmin=-3, xmax=3, ymin=-3, ymax=3, axes_labels=['$U$', '$V$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may add to the graph the singularity $r=0$ as a Boyer-Lindquist chart plot with $(r,\\theta,\\phi)$ fixed at $(0, \\pi/2, 0)$. Similarly, we add the event horizon $r=2m$ as a Boyer-Lindquist chart plot with $(r,\\theta,\\phi)$ fixed at $(2.00001m, \\pi/2, 0)$:
" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 54 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_r0 = X_II.plot(X_KS, fixed_coords={r:0, th:pi/2, ph:0}, ambient_coords=(U,V),\n", " color='yellow', thickness=3, parameters={m:1})\n", "graph_r2 = X_I.plot(X_KS, ranges={t:(-40,40)}, fixed_coords={r:2.00001, th:pi/2, ph:0},\n", " ambient_coords=(U,V), color='black', thickness=2, parameters={m:1})\n", "show(graphI+graphII+graph_r0+graph_r2, xmin=-3, xmax=3, ymin=-3, ymax=3, \n", " axes_labels=['$U$', '$V$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first get the change of coordinates $(v,r,\\theta,\\phi) \\mapsto (U,V,\\theta,\\phi)$ by composing the change $(v,r,\\theta,\\phi) \\mapsto (t,r,\\theta,\\phi)$ with $(t,r,\\theta,\\phi) \\mapsto (U,V,\\theta,\\phi)$:
" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Change of coordinates from Chart (R_I, (v, r, th, ph)) to Chart (R_I, (U, V, th, ph))" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_EF_KS_I = ch_BL_KS_I * ch_EF_BL_I\n", "ch_EF_KS_I" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "U = 1/2*sqrt(2)*sqrt(-2*m + r)*cosh(1/4*(2*m*log(2) + 2*m*log(m) - 2*m*log(-2*m + r) - r + v)/m)*e^(1/4*r/m)/sqrt(m)\n", "V = 1/2*sqrt(2)*sqrt(-2*m + r)*e^(1/4*r/m)*sinh(1/4*(2*m*log(2) + 2*m*log(m) - 2*m*log(-2*m + r) - r + v)/m)/sqrt(m)\n", "th = th\n", "ph = ph" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_EF_KS_I.display()" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Change of coordinates from Chart (R_II, (v, r, th, ph)) to Chart (R_II, (U, V, th, ph))" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_EF_KS_II = ch_BL_KS_II * ch_EF_BL_II\n", "ch_EF_KS_II" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 54 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphI_EF = X_EF_I.plot(X_KS, ranges={v:(-12,12), r:(2.001,5)}, number_values={v:17, r:9},\n", " fixed_coords={th:pi/2,ph:0}, ambient_coords=(U,V),\n", " style={v:'--', r:'-'}, parameters={m:1})\n", "graphII_EF = X_EF_II.plot(X_KS, ranges={v:(-12,12), r:(0.001,1.999)}, number_values={v:17, r:9},\n", " fixed_coords={th:pi/2,ph:0}, ambient_coords=(U,V),\n", " style={v:'--', r:'-'}, color='green', parameters={m:1})\n", "show(graphI_EF+graphII_EF+graph_r0+graph_r2, xmin=-3, xmax=3, ymin=-3, ymax=3,\n", " axes_labels=['$U$', '$V$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are now 9 charts defined on the spacetime manifold:
" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (R_I_union_R_II, (t, r, th, ph)),\n", " Chart (R_I, (t, r, th, ph)),\n", " Chart (R_II, (t, r, th, ph)),\n", " Chart (R_I_union_R_II, (v, r, th, ph)),\n", " Chart (R_I, (v, r, th, ph)),\n", " Chart (R_II, (v, r, th, ph)),\n", " Chart (R_I_union_R_II_union_R_III_union_R_IV, (U, V, th, ph)),\n", " Chart (R_I, (U, V, th, ph)),\n", " Chart (R_II, (U, V, th, ph))]" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.atlas()" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "9" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(M.atlas())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 8 explicit coordinate changes (the coordinate change KS $\\rightarrow$ BL is not known in explicit form):
" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "{(Chart (R_I, (v, r, th, ph)),\n", " Chart (R_I, (U, V, th, ph))): Change of coordinates from Chart (R_I, (v, r, th, ph)) to Chart (R_I, (U, V, th, ph)),\n", " (Chart (R_I, (v, r, th, ph)),\n", " Chart (R_I, (t, r, th, ph))): Change of coordinates from Chart (R_I, (v, r, th, ph)) to Chart (R_I, (t, r, th, ph)),\n", " (Chart (R_II, (v, r, th, ph)),\n", " Chart (R_II, (U, V, th, ph))): Change of coordinates from Chart (R_II, (v, r, th, ph)) to Chart (R_II, (U, V, th, ph)),\n", " (Chart (R_II, (v, r, th, ph)),\n", " Chart (R_II, (t, r, th, ph))): Change of coordinates from Chart (R_II, (v, r, th, ph)) to Chart (R_II, (t, r, th, ph)),\n", " (Chart (R_II, (t, r, th, ph)),\n", " Chart (R_II, (U, V, th, ph))): Change of coordinates from Chart (R_II, (t, r, th, ph)) to Chart (R_II, (U, V, th, ph)),\n", " (Chart (R_II, (t, r, th, ph)),\n", " Chart (R_II, (v, r, th, ph))): Change of coordinates from Chart (R_II, (t, r, th, ph)) to Chart (R_II, (v, r, th, ph)),\n", " (Chart (R_I, (t, r, th, ph)),\n", " Chart (R_I, (U, V, th, ph))): Change of coordinates from Chart (R_I, (t, r, th, ph)) to Chart (R_I, (U, V, th, ph)),\n", " (Chart (R_I, (t, r, th, ph)),\n", " Chart (R_I, (v, r, th, ph))): Change of coordinates from Chart (R_I, (t, r, th, ph)) to Chart (R_I, (v, r, th, ph))}" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.coord_changes()" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "8" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(M.coord_changes())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 10 vector frames (among which 9 coordinate frames):
" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I_union_R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Vector frame (R_I, (e_0,e_1,e_2,e_3)),\n", " Coordinate frame (R_I_union_R_II_union_R_III_union_R_IV, (d/dU,d/dV,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dU,d/dV,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dU,d/dV,d/dth,d/dph))]" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.frames()" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "10" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(M.frames())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 14 fields of tangent space automorphisms expressing the changes of coordinate bases and tetrad:
" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "14" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(M.changes_of_frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thanks to these changes of frames, the components of the metric tensor with respect to the Kruskal-Szekeres can be computed by the method display() and are found to be:
" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = 32*m^3*e^(-1/2*r/m)/r dU*dU - 32*m^3*e^(-1/2*r/m)/r dV*dV + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_KS_I.frame())" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ 32*m^3*e^(-1/2*r/m)/r 0 0 0]\n", "[ 0 -32*m^3*e^(-1/2*r/m)/r 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[X_KS_I.frame(),:]" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = 32*m^3*e^(-1/2*r/m)/r dU*dU - 32*m^3*e^(-1/2*r/m)/r dV*dV + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_KS_II.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first vector of the orthonormal tetrad $e$ expressed on the Kruskal-Szekeres frame:
" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_0 = 1/8*sqrt(2)*sqrt(r)*e^(1/4*r/m)*sinh(1/4*t/m)/m^(3/2) d/dU + 1/8*sqrt(2)*sqrt(r)*cosh(1/4*t/m)*e^(1/4*r/m)/m^(3/2) d/dV" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[0].display(X_KS_I.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann curvature tensor in terms of the Kruskal-Szekeres coordinates:
" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g) = -64*m^4*e^(-1/2*r/m)/r^4 d/dU*dV*dU*dV + 64*m^4*e^(-1/2*r/m)/r^4 d/dU*dV*dV*dU - m/r d/dU*dth*dU*dth + m/r d/dU*dth*dth*dU - m*sin(th)^2/r d/dU*dph*dU*dph + m*sin(th)^2/r d/dU*dph*dph*dU - 64*m^4*e^(-1/2*r/m)/r^4 d/dV*dU*dU*dV + 64*m^4*e^(-1/2*r/m)/r^4 d/dV*dU*dV*dU - m/r d/dV*dth*dV*dth + m/r d/dV*dth*dth*dV - m*sin(th)^2/r d/dV*dph*dV*dph + m*sin(th)^2/r d/dV*dph*dph*dV + 32*m^4*e^(-1/2*r/m)/r^4 d/dth*dU*dU*dth - 32*m^4*e^(-1/2*r/m)/r^4 d/dth*dU*dth*dU - 32*m^4*e^(-1/2*r/m)/r^4 d/dth*dV*dV*dth + 32*m^4*e^(-1/2*r/m)/r^4 d/dth*dV*dth*dV + 2*m*sin(th)^2/r d/dth*dph*dth*dph - 2*m*sin(th)^2/r d/dth*dph*dph*dth + 32*m^4*e^(-1/2*r/m)/r^4 d/dph*dU*dU*dph - 32*m^4*e^(-1/2*r/m)/r^4 d/dph*dU*dph*dU - 32*m^4*e^(-1/2*r/m)/r^4 d/dph*dV*dV*dph + 32*m^4*e^(-1/2*r/m)/r^4 d/dph*dV*dph*dV - 2*m/r d/dph*dth*dth*dph + 2*m/r d/dph*dth*dph*dth" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.riemann().display(X_KS_I.frame())" ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g)^U_V,U,V = -64*m^4*e^(-1/2*r/m)/r^4 \n", "Riem(g)^U_th,U,th = -m/r \n", "Riem(g)^U_ph,U,ph = -m*sin(th)^2/r \n", "Riem(g)^V_U,U,V = -64*m^4*e^(-1/2*r/m)/r^4 \n", "Riem(g)^V_th,V,th = -m/r \n", "Riem(g)^V_ph,V,ph = -m*sin(th)^2/r \n", "Riem(g)^th_U,U,th = 32*m^4*e^(-1/2*r/m)/r^4 \n", "Riem(g)^th_V,V,th = -32*m^4*e^(-1/2*r/m)/r^4 \n", "Riem(g)^th_ph,th,ph = 2*m*sin(th)^2/r \n", "Riem(g)^ph_U,U,ph = 32*m^4*e^(-1/2*r/m)/r^4 \n", "Riem(g)^ph_V,V,ph = -32*m^4*e^(-1/2*r/m)/r^4 \n", "Riem(g)^ph_th,th,ph = -2*m/r " ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.riemann().display_comp(X_KS_I.frame(), only_nonredundant=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The curvature 2-form $\\Omega^0_{\\ \\, 1}$ associated to the Kruskal-Szekeres coordinate frame:
" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form curvature (0,1) of connection nabla_g w.r.t. Coordinate frame (R_I, (d/dU,d/dV,d/dth,d/dph)) on the Open subset R_I of the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "om = g.connection().curvature_form(0,1, X_KS_I.frame()) ; print(om)" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "curvature (0,1) of connection nabla_g w.r.t. Coordinate frame (R_I, (d/dU,d/dV,d/dth,d/dph)) = -64*m^4*e^(-1/2*r/m)/r^4 dU/\\dV" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "om.display(X_KS_I.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now introduce isotropic coordinates $(t,\\bar{r},\\theta,\\varphi)$ on the spacetime manifold:
" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset R_I_union_R_III of the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "regI_III = regI.union(regIII) ; regI_III" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (R_I_union_R_III, (t, ri, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R_I_union_R_III, (t, ri, th, ph))" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_iso.The transformation from the isotropic coordinates to the Boyer-Lindquist ones:
" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (R_I, (t, ri, th, ph)) to Chart (R_I, (t, r, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "r = 1/4*ri*(m/ri + 2)^2\n", "th = th\n", "ph = ph" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assume(2*ri>m) # we consider only region I\n", "ch_iso_BL_I = X_iso_I.transition_map(X_I, [t, ri*(1+m/(2*ri))^2, th, ph])\n", "print(ch_iso_BL_I)\n", "ch_iso_BL_I.display()" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " t == t\n", " ri == ri\n", " th == th\n", " ph == ph\n", " t == t\n", " r == r\n", " th == th\n", " ph == ph\n" ] } ], "source": [ "assume(r>2*m) # we consider only region I\n", "ch_iso_BL_I.set_inverse(t, (r-m+sqrt(r*(r-2*m)))/2, th, ph, verbose=True)" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "ri = -1/2*m + 1/2*r + 1/2*sqrt(-(2*m - r)*r)\n", "th = th\n", "ph = ph" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_iso_BL_I.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this stage, 11 charts have been defined on the manifold $\\mathcal{M}$:
" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (R_I_union_R_II, (t, r, th, ph)),\n", " Chart (R_I, (t, r, th, ph)),\n", " Chart (R_II, (t, r, th, ph)),\n", " Chart (R_I_union_R_II, (v, r, th, ph)),\n", " Chart (R_I, (v, r, th, ph)),\n", " Chart (R_II, (v, r, th, ph)),\n", " Chart (R_I_union_R_II_union_R_III_union_R_IV, (U, V, th, ph)),\n", " Chart (R_I, (U, V, th, ph)),\n", " Chart (R_II, (U, V, th, ph)),\n", " Chart (R_I_union_R_III, (t, ri, th, ph)),\n", " Chart (R_I, (t, ri, th, ph))]" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.atlas()" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "11" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(M.atlas())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "12 vector frames have been defined on $\\mathcal{M}$: 11 coordinate bases and the tetrad $(e_\\alpha)$:
" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate frame (R_I_union_R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dt,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I_union_R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dv,d/dr,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dv,d/dr,d/dth,d/dph)),\n", " Vector frame (R_I, (e_0,e_1,e_2,e_3)),\n", " Coordinate frame (R_I_union_R_II_union_R_III_union_R_IV, (d/dU,d/dV,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dU,d/dV,d/dth,d/dph)),\n", " Coordinate frame (R_II, (d/dU,d/dV,d/dth,d/dph)),\n", " Coordinate frame (R_I_union_R_III, (d/dt,d/dri,d/dth,d/dph)),\n", " Coordinate frame (R_I, (d/dt,d/dri,d/dth,d/dph))]" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.frames()" ] }, { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "12" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(M.frames())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components of the metric tensor in terms of the isotropic coordinates are given by
" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -(m^2 - 4*m*ri + 4*ri^2)/(m^2 + 4*m*ri + 4*ri^2) dt*dt + 1/16*(m^4 + 8*m^3*ri + 24*m^2*ri^2 + 32*m*ri^3 + 16*ri^4)/ri^4 dri*dri + 1/16*(m^4 + 8*m^3*ri + 24*m^2*ri^2 + 32*m*ri^3 + 16*ri^4)/ri^2 dth*dth + 1/16*(m^4 + 8*m^3*ri + 24*m^2*ri^2 + 32*m*ri^3 + 16*ri^4)*sin(th)^2/ri^2 dph*dph" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_iso_I.frame(), X_iso_I)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $g_{00}$ component can be factorized:
" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-(m^2 - 4*m*ri + 4*ri^2)/(m^2 + 4*m*ri + 4*ri^2)" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[X_iso_I.frame(), 0,0, X_iso_I]" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-(m - 2*ri)^2/(m + 2*ri)^2" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[X_iso_I.frame(), 0,0, X_iso_I].factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us also factorize the other components:
" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [], "source": [ "for i in range(1,4):\n", " g[X_iso_I.frame(), i,i, X_iso_I].factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The output of the display() command looks nicer:
" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -(m - 2*ri)^2/(m + 2*ri)^2 dt*dt + 1/16*(m + 2*ri)^4/ri^4 dri*dri + 1/16*(m + 2*ri)^4/ri^2 dth*dth + 1/16*(m + 2*ri)^4*sin(th)^2/ri^2 dph*dph" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_iso_I.frame(), X_iso_I)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expression of the tetrad associated with the static observer in terms of the isotropic coordinate basis:
" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_0 = -(m + 2*ri)/(m - 2*ri) d/dt" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[0].display(X_iso_I.frame(), X_iso_I)" ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_1 = 4*ri^2/(m^2 + 4*m*ri + 4*ri^2) d/dri" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display(X_iso_I.frame(), X_iso_I)" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_2 = 4*ri/(m^2 + 4*m*ri + 4*ri^2) d/dth" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display(X_iso_I.frame(), X_iso_I)" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_3 = 4*ri/((m^2 + 4*m*ri + 4*ri^2)*sin(th)) d/dph" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[3].display(X_iso_I.frame(), X_iso_I)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.2", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 1 }