{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Anti-de Sitter spacetime\n", "\n", "This notebook demonstrates a few capabilities of SageMath in computations regarding the 4-dimensional anti-de Sitter spacetime. The corresponding tools have been developed within the [SageManifolds](https://sagemanifolds.obspm.fr) project." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 8.2 is required to run this notebook:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.0.beta3, Release Date: 2019-10-26'" ] }, "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": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics and initialize a time counter for benchmarking:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', 'jmol', 'tachyon' or None (default)\n", "import time\n", "comput_time0 = time.perf_counter()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime manifold\n", "\n", "We declare the anti-de Sitter spacetime as a 4-dimensional Lorentzian manifold:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "4-dimensional Lorentzian manifold M" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = Manifold(4, 'M', r'\\mathcal{M}', structure='Lorentzian')\n", "print(M); M" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We consider hyperbolic coordinates $(\\tau,\\rho,\\theta,\\phi)$ on $\\mathcal{M}$. Allowing for the standard coordinate singularities at $\\rho=0$, $\\theta=0$ or $\\theta=\\pi$, these coordinates cover the entire spacetime manifold (which is topologically $\\mathbb{R}^4$). If we restrict ourselves to regular coordinates (i.e. to considering only mathematically well defined charts), the hyperbolic coordinates cover only an open part of $\\mathcal{M}$, which we call $\\mathcal{M}_0$, on which $\\rho$ spans the open interval $(0,+\\infty)$, $\\theta$ the open interval $(0,\\pi)$ and $\\phi$ the open interval $(0,2\\pi)$. Therefore, we declare:

" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (M_0, (ta, rh, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M_0, (ta, rh, th, ph))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M0 = M.open_subset('M_0', r'\\mathcal{M}_0' )\n", "X_hyp. = M0.chart(r'ta:\\tau rh:(0,+oo):\\rho th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "print(X_hyp); X_hyp" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "ta: (-oo, +oo); rh: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\mathbb{R}^{2,3}$ as an ambient space\n", "The AdS metric can be defined as that induced by the immersion of $\\mathcal{M}$ in $\\mathbb{R}^{2,3}$, the latter being nothing but $\\mathbb{R}^5$ equipped with a flat pseudo-Riemannian metric of signature $(-,-,+,+,+)$. Let us construct $\\mathbb{R}^{2,3}$ as a 5-dimensional manifold covered by canonical coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (R23, (U, V, X, Y, Z))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R23, (U, V, X, Y, Z))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R23 = Manifold(5, 'R23', r'\\mathbb{R}^{2,3}', structure='pseudo-Riemannian', signature=1, \n", " metric_name='h')\n", "X23. = R23.chart()\n", "print(X23); X23" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the pseudo-Riemannian metric of $\\mathbb{R}^{2,3}$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "h = -dU*dU - dV*dV + dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = R23.metric()\n", "h[0,0], h[1,1], h[2,2], h[3,3], h[4,4] = -1, -1, 1, 1, 1\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The AdS immersion into $\\mathbb{R}^{2,3}$ is defined as a differential map $\\Phi$ from $\\mathcal{M}$ to $\\mathbb{R}^{2,3}$, by providing its expression in terms of $\\mathcal{M}$'s default chart (which is X_hyp = $(\\mathcal{M}_0,(\\tau,\\rho,\\theta,\\phi))$ ) and $\\mathbb{R}^{2,3}$'s default chart (which is X23 = $(\\mathbb{R}^{2,3},(U,V,X,Y,Z))$ ):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Phi from the 4-dimensional Lorentzian manifold M to the 5-dimensional pseudo-Riemannian manifold R23\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Phi: M --> R23\n", "on M_0: (ta, rh, th, ph) |--> (U, V, X, Y, Z) = (l*cos(ta/l)*cosh(rh), l*cosh(rh)*sin(ta/l), l*cos(ph)*sin(th)*sinh(rh), l*sin(ph)*sin(th)*sinh(rh), l*cos(th)*sinh(rh))" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('l', latex_name=r'\\ell', domain='real')\n", "assume(l>0)\n", "Phi = M.diff_map(R23, [l*cosh(rh)*cos(ta/l),\n", " l*cosh(rh)*sin(ta/l),\n", " l*sinh(rh)*sin(th)*cos(ph),\n", " l*sinh(rh)*sin(th)*sin(ph),\n", " l*sinh(rh)*cos(th)],\n", " name='Phi', latex_name=r'\\Phi')\n", "print(Phi); Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The constant $\\ell$ is the AdS length parameter. Considering AdS metric as a solution of vacuum Einstein equation with negative cosmological constant $\\Lambda$, one has $\\ell = \\sqrt{-3/\\Lambda}$.\n", "\n", "Let us evaluate the image of a point via the map $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point p on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "p = M((ta, rh, th, ph), name='p'); print(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coordinates of $p$ in the chart `X_hyp`:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(ta, rh, th, ph)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp(p)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(p) on the 5-dimensional pseudo-Riemannian manifold R23\n" ] } ], "source": [ "q = Phi(p); print(q)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(l*cos(ta/l)*cosh(rh),\n", " l*cosh(rh)*sin(ta/l),\n", " l*cos(ph)*sin(th)*sinh(rh),\n", " l*sin(ph)*sin(th)*sinh(rh),\n", " l*cos(th)*sinh(rh))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X23(q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The image of $\\mathcal{M}$ by the immersion $\\Phi$ is a hyperboloid of one sheet, of equation $$-U^2-V^2+X^2+Y^2+Z^2=-\\ell^2.$$\n", "Indeed:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-l^2" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Uq,Vq,Xq,Yq,Zq) = X23(q)\n", "s = - Uq^2 - Vq^2 + Xq^2 + Yq^2 + Zq^2\n", "s.simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may use the immersion $\\Phi$ to draw the coordinate grid $(\\tau,\\rho)$ in terms of the coordinates $(U,V,X)$ for $\\theta=\\pi/2$ and $\\phi=0$ ($X\\geq 0$ part) or $\\phi=\\pi$ \n", "($X\\leq 0$ part). The red (rep. grey) curves are those for which $\\rho={\\rm const}$ \n", "(resp. $\\tau={\\rm const}$):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_hyp = X_hyp.plot(X23, mapping=Phi, ambient_coords=(V,X,U), fixed_coords={th:pi/2, ph:0}, \n", " ranges={ta:(0,2*pi), rh:(0,2)}, number_values=9, \n", " color={ta:'red', rh:'grey'}, thickness=2, parameters={l:1}, \n", " label_axes=False) # phi = 0 => X > 0 part\n", "graph_hyp += X_hyp.plot(X23, mapping=Phi, ambient_coords=(V,X,U), fixed_coords={th:pi/2, ph:pi},\n", " ranges={ta:(0,2*pi), rh:(0,2)}, number_values=9, \n", " color={ta:'red', rh:'grey'}, thickness=2, parameters={l:1}, \n", " label_axes=False) # phi = pi => X < 0 part\n", "show(graph_hyp, aspect_ratio=1, viewer=viewer3D, \n", " axes_labels=['V','X','U'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To have a nicer picture, we add the plot of the hyperboloid obtained by `parametric_plot` with $(\\tau,\\rho)$ as parameters and the expressions of $(U,V,X)$ in terms of $(\\tau,\\rho)$ deduced from the coordinate representation of $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate functions (l*cos(ta/l)*cosh(rh), l*cosh(rh)*sin(ta/l), l*cos(ph)*sin(th)*sinh(rh), l*sin(ph)*sin(th)*sinh(rh), l*cos(th)*sinh(rh)) on the Chart (M_0, (ta, rh, th, ph))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.coord_functions() # the default pair of charts (X_hyp, X23) is assumed" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(cos(ta)*cosh(rh), cosh(rh)*sin(ta), sinh(rh))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ug = Phi.coord_functions()[0](ta,rh,pi/2,0).subs({l:1}) # l=1 substituted to have numerical values\n", "Vg = Phi.coord_functions()[1](ta,rh,pi/2,0).subs({l:1})\n", "Xg = Phi.coord_functions()[2](ta,rh,pi/2,0).subs({l:1})\n", "Ug, Vg, Xg" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hyperboloid = parametric_plot3d([Vg, Xg, Ug], (ta,0,2*pi), (rh,-2,2), color=(1.,1.,0.9))\n", "graph_hyp += hyperboloid\n", "show(graph_hyp, aspect_ratio=1, viewer=viewer3D,\n", " axes_labels=['V','X','U'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime metric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As mentionned above, the AdS metric $g$ on $\\mathcal{M}$ is that induced by the flat metric $h$ on $\\mathbb{R}^{2,3}$, i.e.$g$ is the pullback of $h$ by the differentiable map $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "g = M.metric()\n", "g.set( Phi.pullback(h) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The expression of $g$ in terms of $\\mathcal{M}$'s default frame is found to be

" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -cosh(rh)^2 dta*dta + l^2 drh*drh + l^2*sinh(rh)^2 dth*dth + l^2*sin(th)^2*sinh(rh)^2 dph*dph" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ -cosh(rh)^2 0 0 0]\n", "[ 0 l^2 0 0]\n", "[ 0 0 l^2*sinh(rh)^2 0]\n", "[ 0 0 0 l^2*sin(th)^2*sinh(rh)^2]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curvature

\n", "

The Riemann tensor of $g$ is

" ] }, { "cell_type": "code", "execution_count": 22, "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": [ "Riem = g.riemann()\n", "print(Riem)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g)^ta_rh,ta,rh = -1 \n", "Riem(g)^ta_th,ta,th = -sinh(rh)^2 \n", "Riem(g)^ta_ph,ta,ph = -sin(th)^2*sinh(rh)^2 \n", "Riem(g)^rh_ta,ta,rh = -cosh(rh)^2/l^2 \n", "Riem(g)^rh_th,rh,th = -sinh(rh)^2 \n", "Riem(g)^rh_ph,rh,ph = -sin(th)^2*sinh(rh)^2 \n", "Riem(g)^th_ta,ta,th = -cosh(rh)^2/l^2 \n", "Riem(g)^th_rh,rh,th = 1 \n", "Riem(g)^th_ph,th,ph = -sin(th)^2*sinh(rh)^2 \n", "Riem(g)^ph_ta,ta,ph = -cosh(rh)^2/l^2 \n", "Riem(g)^ph_rh,rh,ph = 1 \n", "Riem(g)^ph_th,th,ph = sinh(rh)^2 " ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(only_nonredundant=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ricci tensor:

" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms Ric(g) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Ric(g) = 3*cosh(rh)^2/l^2 dta*dta - 3 drh*drh - 3*sinh(rh)^2 dth*dth - 3*sin(th)^2*sinh(rh)^2 dph*dph" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "print(Ric)\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ 3*cosh(rh)^2/l^2 0 0 0]\n", "[ 0 -3 0 0]\n", "[ 0 0 -3*sinh(rh)^2 0]\n", "[ 0 0 0 -3*sin(th)^2*sinh(rh)^2]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ricci scalar:

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field r(g) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "r(g): M --> R\n", "on M_0: (ta, rh, th, ph) |--> -12/l^2" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "print(R)\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We recover the fact that AdS spacetime has a constant curvature. It is indeed a **maximally symmetric space**. In particular, the Riemann tensor is expressible as\n", "$$ R^i_{\\ \\, jlk} = \\frac{R}{n(n-1)} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right), $$\n", "where $n$ is the dimension of $\\mathcal{M}$: $n=4$ in the present case. Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -\\frac{R}{6} g_{j[k} \\delta^i_{\\ \\, l]}$:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = M.tangent_identity_field() \n", "Riem == - (R/6)*(g*delta).antisymmetrize(2,3) # 2,3 = last positions of the \n", " # type-(1,3) tensor g*delta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may also check that AdS metric is a solution of the vacuum **Einstein equation** with (negative) cosmological constant $\\Lambda = - 3/\\ell^2$:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Lambda = -3/l^2\n", "Ric - 1/2*R*g + Lambda*g == 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Radial null geodesics\n", "\n", "Null geodesics that are radial with respect to coordinates $(\\tau,\\rho,\\theta,\\phi)$ obey\n", "$$ \\tau = \\pm 2 \\ell \\left( \\mathrm{atan} \\left(\\mathrm{e}^\\rho\\right) - \\frac{\\pi}{4} \\right) + \\tau_0,$$\n", "where $\\tau_0$ is a constant (the value of $\\tau$ at $\\rho=0$). Note that, due to the homogeneity of AdS spacetime, any null geodesic is a \"radial\" geodesic with respect to some coordinate system $(\\tau',\\rho',\\theta',\\phi')$, as in Minkowski spacetime, any null geodesic is a straight line and one can always find a Minkowskian coordinate system $(t',x',y',z')$ with respect to which the null geodesic is radial.\n", "\n", "Let us consider two finite families of radial null geodesics having $\\theta=\\pi/2$ and $\\phi=0$ or $\\pi$: \n", "- `null_geod1` has $\\phi=\\pi$ when $\\tau< 0$ and $\\phi=0$ when $\\tau>0$\n", "- `null_geod2` has $\\phi=0$ when $\\tau<0$ and $\\phi=\\pi$ when $\\tau>0$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "lamb = var('lamb', latex_name=r'\\lambda')\n", "null_geod1 = [M.curve({X_hyp: [2*sgn(lamb)*l*(atan(exp(abs(lamb))) - pi/4) + 2*pi*(i-4)/8, \n", " abs(lamb), pi/2, pi*unit_step(-lamb)]}, \n", " (lamb, -oo, +oo)) for i in range(9)]\n", "null_geod2 = [M.curve({X_hyp: [2*sgn(lamb)*l*(atan(exp(abs(lamb))) - pi/4) + 2*pi*(i-4)/8, \n", " abs(lamb), pi/2, pi*unit_step(lamb)]}, \n", " (lamb, -oo, +oo)) for i in range(9)]\n", "null_geods = null_geod1 + null_geod2" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Curve in the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "print(null_geods[0])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "R --> M\n", " lamb |--> (ta, rh, th, ph) = (-pi - 1/2*(pi - 4*arctan(e^abs(lamb)))*l*sgn(lamb), abs(lamb), 1/2*pi, pi*unit_step(-lamb))" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "null_geods[0].display()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "R --> M\n", " lamb |--> (ta, rh, th, ph) = (-pi - 1/2*(pi - 4*arctan(e^abs(lamb)))*l*sgn(lamb), abs(lamb), 1/2*pi, pi*unit_step(lamb))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "null_geods[9].display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To graphically display these geodesics, we introduce a Cartesian-like coordinate system\n", "$(\\tau,x_\\rho,y_\\rho,z_\\rho)$ linked to $(\\tau,\\rho,\\theta,\\phi)$ by the standard formulas:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "ta = ta\n", "x_rho = rh*cos(ph)*sin(th)\n", "y_rho = rh*sin(ph)*sin(th)\n", "z_rho = rh*cos(th)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp_graph. = M0.chart(r'ta:\\tau x_rho:x_\\rho y_rho:y_\\rho z_rho:z_\\rho')\n", "hyp_to_hyp_graph = X_hyp.transition_map(X_hyp_graph, [ta, rh*sin(th)*cos(ph), \n", " rh*sin(th)*sin(ph), rh*cos(th)])\n", "hyp_to_hyp_graph.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the null geodesics in terms of the coordinates $(\\tau,x_\\rho)$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 36 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_2d = Graphics()\n", "for geod in null_geods:\n", " geod.expr(geod.domain().canonical_chart(), X_hyp_graph)\n", " graph_2d += geod.plot(X_hyp_graph, ambient_coords=(x_rho,ta), prange=(-4,4),\n", " parameters={l:1}, color='green', thickness=1.5)\n", "graph_2d += X_hyp_graph.plot(X_hyp_graph, ambient_coords=(x_rho,ta), \n", " fixed_coords={th:0, ph:pi}, \n", " ranges={ta:(-pi,pi), x_rho:(-4,4)}, \n", " number_values={ta: 9, x_rho: 9},\n", " color={ta:'red', x_rho:'grey'}, parameters={l:1})\n", "show(graph_2d, aspect_ratio=1, ymin=-pi, ymax=pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also get a 3D view of the radial null geodesics via the isometric immersion $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "