{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Anti-de Sitter spacetime\n", "\n", "This worksheet demonstrates a few capabilities of [SageManifolds](http://sagemanifolds.obspm.fr) (version 1.0, as included in SageMath 7.5) in computations regarding the 4-dimensional anti-de Sitter spacetime.\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.0/SM_AdS.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath within the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.0.beta12, Release Date: 2017-06-22'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "First we set up the notebook to display mathematical objects using LaTeX rendering:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', 'jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Spacetime manifold\n", "\n", "We declare the anti-de Sitter spacetime as a 4-dimensional differentiable manifold:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional differentiable manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "4-dimensional differentiable manifold M" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = Manifold(4, 'M', r'\\mathcal{M}')\n", "print(M); M" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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}')\n", "X23. = R23.chart()\n", "print(X23); X23" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We introduce on $\\mathbb{R}^{2,3}$ the flat pseudo-Riemannian metric $h$ of signature $(-,-,+,+,+)$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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('h', signature=1)\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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Phi from the 4-dimensional differentiable manifold M to the 5-dimensional differentiable 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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point p on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "p = M((ta, rh, th, ph), name='p'); print(p)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The coordinates of $p$ in the chart `X_hyp`:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(p) on the 5-dimensional differentiable manifold R23\n" ] } ], "source": [ "q = Phi(p); print(q)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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, online=True,\n", " axes_labels=['V','X','U'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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, online=True,\n", " axes_labels=['V','X','U'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Spacetime metric" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "g = M.lorentzian_metric('g')\n", "g.set( Phi.pullback(h) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

Curvature

\n", "

The Riemann tensor of $g$ is

" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "Riem = g.riemann()\n", "print(Riem)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

The Ricci tensor:

" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms Ric(g) on the 4-dimensional differentiable 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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

The Ricci scalar:

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field r(g) on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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 type-(1,3) tensor g*delta" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Curve in the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "print(null_geods[0])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "Let us plot the null geodesics in terms of the coordinates $(\\tau,x_\\rho)$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtgAAAJFCAYAAADnK4CYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "\n", "