{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simon-Mars tensor in Curzon-Chazy spacetime\n", "\n", "This notebook demonstrates a few capabilities of SageMath in computations regarding Curzon-Chazy spacetime. It implements the computation of the Simon-Mars tensor of Curzon-Chazy spacetime used in the article [arXiv:1412.6542](http://arxiv.org/abs/1412.6542). The corresponding tools have been developed within the [SageManifolds](https://sagemanifolds.obspm.fr) project (version 1.3, as included in SageMath 8.3).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.3/SM_Simon-Mars_Curzon-Chazy.ipynb) to download the notebook 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 notebook:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.3, Release Date: 2018-08-03'" ] }, "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 Curzon-Chazy spacetime as a 4-dimensional Lorentzian manifold:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M', latex_name=r'\\mathcal{M}', structure='Lorentzian')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We introduce the coordinates $(t,r,y,\\phi)$ with $y$ related to the standard Weyl-Papapetrou coordinates $(t,r,\\theta,\\phi)$ by $y=\\cos\\theta$:

" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (M, (t, r, y, ph))\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathcal{M},(t, r, y, {\\phi})\\right)$ " ], "text/plain": [ "Chart (M, (t, r, y, ph))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X. = M.chart(r't r:(0,+oo) y:(-1,1) ph:(0,2*pi):\\phi') \n", "print(X) ; X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Metric tensor

\n", "

We declare the only parameter of the Curzon-Chazy spacetime, which is the mass $m$ as a symbolic variable:

" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}m$ " ], "text/plain": [ "m" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('m')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Without any loss of generality, we set $m$ to some specific value (this amounts simply to fixing some length scale):

" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "m = 12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us set the components of the spacetime metric in the coordinate frame associated with Weyl-Papapetrou coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "g = M.metric()\n", "g[0,0] = - exp(-2*m/r)\n", "g[1,1] = exp(2*m/r-m^2*(1-y^2)/r^2)\n", "g[2,2] = exp(2*m/r-m^2*(1-y^2)/r^2)*r^2/(1-y^2)\n", "g[3,3] = exp(2*m/r)*r^2*(1-y^2)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-e^{\\left(-\\frac{24}{r}\\right)} & 0 & 0 & 0 \\\\\n", "0 & e^{\\left(\\frac{144 \\, {\\left(y^{2} - 1\\right)}}{r^{2}} + \\frac{24}{r}\\right)} & 0 & 0 \\\\\n", "0 & 0 & -\\frac{r^{2} e^{\\left(\\frac{144 \\, {\\left(y^{2} - 1\\right)}}{r^{2}} + \\frac{24}{r}\\right)}}{y^{2} - 1} & 0 \\\\\n", "0 & 0 & 0 & -{\\left(y^{2} - 1\\right)} r^{2} e^{\\frac{24}{r}}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[ -e^(-24/r) 0 0 0]\n", "[ 0 e^(144*(y^2 - 1)/r^2 + 24/r) 0 0]\n", "[ 0 0 -r^2*e^(144*(y^2 - 1)/r^2 + 24/r)/(y^2 - 1) 0]\n", "[ 0 0 0 -(y^2 - 1)*r^2*e^(24/r)]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Levi-Civita connection $\\nabla$ associated with $g$:

" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Levi-Civita connection nabla_g associated with the Lorentzian metric g on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "nab = g.connection() ; print(nab)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

As a check, we verify that the covariant derivative of $g$ with respect to $\\nabla$ vanishes identically:

" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} g = 0$ " ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Killing vector

\n", "

The default vector frame on the spacetime manifold is the coordinate basis associated with Weyl-Papapetrou coordinates:

" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.default_frame() is X.frame()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathcal{M}, \\left(\\frac{\\partial}{\\partial t },\\frac{\\partial}{\\partial r },\\frac{\\partial}{\\partial y },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (M, (d/dt,d/dr,d/dy,d/dph))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us consider the first vector field of this frame:

" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t }$ " ], "text/plain": [ "Vector field d/dt on the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi = X.frame()[0] ; xi" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field d/dt on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "print(xi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The 1-form associated to it by metric duality is

" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form xi_form on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{\\xi} = -e^{\\left(-\\frac{24}{r}\\right)} \\mathrm{d} t$ " ], "text/plain": [ "xi_form = -e^(-24/r) dt" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi_form = xi.down(g)\n", "xi_form.set_name('xi_form', r'\\underline{\\xi}')\n", "print(xi_form) ; xi_form.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Its covariant derivative is

" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(xi_form) of type (0,2) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} \\underline{\\xi} = -\\frac{12 \\, e^{\\left(-\\frac{24}{r}\\right)}}{r^{2}} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{12 \\, e^{\\left(-\\frac{24}{r}\\right)}}{r^{2}} \\mathrm{d} r\\otimes \\mathrm{d} t$ " ], "text/plain": [ "nabla_g(xi_form) = -12*e^(-24/r)/r^2 dt*dr + 12*e^(-24/r)/r^2 dr*dt" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab_xi = nab(xi_form)\n", "print(nab_xi) ; nab_xi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us check that the Killing equation is satisfied:

" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab_xi.symmetrize().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Equivalently, we check that the Lie derivative of the metric along $\\xi$ vanishes:

" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.lie_der(xi).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Thank to Killing equation, $\\nabla_g \\underline{\\xi}$ is antisymmetric. We may therefore define a 2-form by $F := - \\nabla_g \\xi$. Here we enforce the antisymmetry by calling the function antisymmetrize() on nab_xi:

" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form F on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}F = \\frac{12 \\, e^{\\left(-\\frac{24}{r}\\right)}}{r^{2}} \\mathrm{d} t\\wedge \\mathrm{d} r$ " ], "text/plain": [ "F = 12*e^(-24/r)/r^2 dt/\\dr" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F = - nab_xi.antisymmetrize()\n", "F.set_name('F')\n", "print(F)\n", "F.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We check that

" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F == - nab_xi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The squared norm of the Killing vector is

" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field lambda on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\lambda:& \\mathcal{M} & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, y, {\\phi}\\right) & \\longmapsto & e^{\\left(-\\frac{24}{r}\\right)} \\end{array}$ " ], "text/plain": [ "lambda: M --> R\n", " (t, r, y, ph) |--> e^(-24/r)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lamb = - g(xi,xi)\n", "lamb.set_name('lambda', r'\\lambda')\n", "print(lamb)\n", "lamb.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Instead of invoking $g(\\xi,\\xi)$, we could have evaluated $\\lambda$ by means of the 1-form $\\underline{\\xi}$ acting on the vector field $\\xi$:

" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lamb == - xi_form(xi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

or we could have used index notation in the form $\\lambda = - \\xi_a \\xi^a$:

" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lamb == - ( xi_form['_a']*xi['^a'] )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curvature

\n", "

The Riemann curvature tensor associated with $g$ is

" ] }, { "cell_type": "code", "execution_count": 24, "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": "markdown", "metadata": {}, "source": [ "

The component $R^0_{\\ \\, 101} = R^t_{\\ \\, rtr}$ is

" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{24 \\, {\\left(r^{2} - 72 \\, y^{2} - 12 \\, r + 72\\right)}}{r^{5}}$ " ], "text/plain": [ "24*(r^2 - 72*y^2 - 12*r + 72)/r^5" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem[0,1,0,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

while the component $R^2_{\\ \\, 323} = R^y_{\\ \\, \\phi y \\phi}$ is

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{24 \\, {\\left(72 \\, y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - {\\left(r^{2} - 12 \\, r + 144\\right)} y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + {\\left(r^{2} - 12 \\, r + 72\\right)} e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{r^{3}}$ " ], "text/plain": [ "24*(72*y^4*e^(144/r^2) - (r^2 - 12*r + 144)*y^2*e^(144/r^2) + (r^2 - 12*r + 72)*e^(144/r^2))*e^(-144*y^2/r^2)/r^3" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem[2,3,2,3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

All the non-vanishing components of the Riemann tensor, taking into account the antisymmetry on the last two indices:

" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, t} \\, r \\, t \\, r }^{ \\, t \\phantom{\\, r} \\phantom{\\, t} \\phantom{\\, r} } & = & \\frac{24 \\, {\\left(r^{2} - 72 \\, y^{2} - 12 \\, r + 72\\right)}}{r^{5}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, t} \\, r \\, t \\, y }^{ \\, t \\phantom{\\, r} \\phantom{\\, t} \\phantom{\\, y} } & = & \\frac{1728 \\, y}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, t} \\, y \\, t \\, r }^{ \\, t \\phantom{\\, y} \\phantom{\\, t} \\phantom{\\, r} } & = & \\frac{1728 \\, y}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, t} \\, y \\, t \\, y }^{ \\, t \\phantom{\\, y} \\phantom{\\, t} \\phantom{\\, y} } & = & \\frac{12 \\, {\\left(r^{2} - 144 \\, y^{2} - 12 \\, r + 144\\right)}}{r^{3} y^{2} - r^{3}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, t} \\, {\\phi} \\, t \\, {\\phi} }^{ \\, t \\phantom{\\, {\\phi}} \\phantom{\\, t} \\phantom{\\, {\\phi}} } & = & \\frac{12 \\, {\\left({\\left(r - 12\\right)} y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} - {\\left(r - 12\\right)} e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{r^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, r} \\, t \\, t \\, r }^{ \\, r \\phantom{\\, t} \\phantom{\\, t} \\phantom{\\, r} } & = & -\\frac{24 \\, {\\left(72 \\, y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} - {\\left(r^{2} - 12 \\, r + 72\\right)} e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{5}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, r} \\, t \\, t \\, y }^{ \\, r \\phantom{\\, t} \\phantom{\\, t} \\phantom{\\, y} } & = & \\frac{1728 \\, y e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r} + \\frac{144}{r^{2}}\\right)}}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, r} \\, y \\, r \\, y }^{ \\, r \\phantom{\\, y} \\phantom{\\, r} \\phantom{\\, y} } & = & \\frac{12 \\, {\\left(r - 12\\right)}}{r^{2} y^{2} - r^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, r} \\, {\\phi} \\, r \\, {\\phi} }^{ \\, r \\phantom{\\, {\\phi}} \\phantom{\\, r} \\phantom{\\, {\\phi}} } & = & -\\frac{12 \\, {\\left(144 \\, y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - {\\left(r^{2} - 12 \\, r + 288\\right)} y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + {\\left(r^{2} - 12 \\, r + 144\\right)} e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{r^{3}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, r} \\, {\\phi} \\, y \\, {\\phi} }^{ \\, r \\phantom{\\, {\\phi}} \\phantom{\\, y} \\phantom{\\, {\\phi}} } & = & \\frac{1728 \\, {\\left(y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} - y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{r^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, t \\, t \\, r }^{ \\, y \\phantom{\\, t} \\phantom{\\, t} \\phantom{\\, r} } & = & -\\frac{1728 \\, {\\left(y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} - y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{6}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, t \\, t \\, y }^{ \\, y \\phantom{\\, t} \\phantom{\\, t} \\phantom{\\, y} } & = & \\frac{12 \\, {\\left(144 \\, y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} - {\\left(r^{2} - 12 \\, r + 144\\right)} e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{5}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, r \\, r \\, y }^{ \\, y \\phantom{\\, r} \\phantom{\\, r} \\phantom{\\, y} } & = & \\frac{12 \\, {\\left(r - 12\\right)}}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, {\\phi} \\, r \\, {\\phi} }^{ \\, y \\phantom{\\, {\\phi}} \\phantom{\\, r} \\phantom{\\, {\\phi}} } & = & -\\frac{1728 \\, {\\left(y^{5} e^{\\left(\\frac{144}{r^{2}}\\right)} - 2 \\, y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} + y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, {\\phi} \\, y \\, {\\phi} }^{ \\, y \\phantom{\\, {\\phi}} \\phantom{\\, y} \\phantom{\\, {\\phi}} } & = & \\frac{24 \\, {\\left(72 \\, y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - {\\left(r^{2} - 12 \\, r + 144\\right)} y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + {\\left(r^{2} - 12 \\, r + 72\\right)} e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{r^{3}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, t \\, t \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, t} \\phantom{\\, t} \\phantom{\\, {\\phi}} } & = & -\\frac{12 \\, {\\left(r - 12\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r} + \\frac{144}{r^{2}}\\right)}}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, r \\, r \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, r} \\phantom{\\, r} \\phantom{\\, {\\phi}} } & = & \\frac{12 \\, {\\left(r^{2} - 144 \\, y^{2} - 12 \\, r + 144\\right)}}{r^{5}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, r \\, y \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, r} \\phantom{\\, y} \\phantom{\\, {\\phi}} } & = & \\frac{1728 \\, y}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, y \\, r \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, y} \\phantom{\\, r} \\phantom{\\, {\\phi}} } & = & \\frac{1728 \\, y}{r^{4}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, y \\, y \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, y} \\phantom{\\, y} \\phantom{\\, {\\phi}} } & = & \\frac{24 \\, {\\left(r^{2} - 72 \\, y^{2} - 12 \\, r + 72\\right)}}{r^{3} y^{2} - r^{3}} \\end{array}$ " ], "text/plain": [ "Riem(g)^t_r,t,r = 24*(r^2 - 72*y^2 - 12*r + 72)/r^5 \n", "Riem(g)^t_r,t,y = 1728*y/r^4 \n", "Riem(g)^t_y,t,r = 1728*y/r^4 \n", "Riem(g)^t_y,t,y = 12*(r^2 - 144*y^2 - 12*r + 144)/(r^3*y^2 - r^3) \n", "Riem(g)^t_ph,t,ph = 12*((r - 12)*y^2*e^(144/r^2) - (r - 12)*e^(144/r^2))*e^(-144*y^2/r^2)/r^2 \n", "Riem(g)^r_t,t,r = -24*(72*y^2*e^(144/r^2) - (r^2 - 12*r + 72)*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^5 \n", "Riem(g)^r_t,t,y = 1728*y*e^(-144*y^2/r^2 - 48/r + 144/r^2)/r^4 \n", "Riem(g)^r_y,r,y = 12*(r - 12)/(r^2*y^2 - r^2) \n", "Riem(g)^r_ph,r,ph = -12*(144*y^4*e^(144/r^2) - (r^2 - 12*r + 288)*y^2*e^(144/r^2) + (r^2 - 12*r + 144)*e^(144/r^2))*e^(-144*y^2/r^2)/r^3 \n", "Riem(g)^r_ph,y,ph = 1728*(y^3*e^(144/r^2) - y*e^(144/r^2))*e^(-144*y^2/r^2)/r^2 \n", "Riem(g)^y_t,t,r = -1728*(y^3*e^(144/r^2) - y*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^6 \n", "Riem(g)^y_t,t,y = 12*(144*y^2*e^(144/r^2) - (r^2 - 12*r + 144)*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^5 \n", "Riem(g)^y_r,r,y = 12*(r - 12)/r^4 \n", "Riem(g)^y_ph,r,ph = -1728*(y^5*e^(144/r^2) - 2*y^3*e^(144/r^2) + y*e^(144/r^2))*e^(-144*y^2/r^2)/r^4 \n", "Riem(g)^y_ph,y,ph = 24*(72*y^4*e^(144/r^2) - (r^2 - 12*r + 144)*y^2*e^(144/r^2) + (r^2 - 12*r + 72)*e^(144/r^2))*e^(-144*y^2/r^2)/r^3 \n", "Riem(g)^ph_t,t,ph = -12*(r - 12)*e^(-144*y^2/r^2 - 48/r + 144/r^2)/r^4 \n", "Riem(g)^ph_r,r,ph = 12*(r^2 - 144*y^2 - 12*r + 144)/r^5 \n", "Riem(g)^ph_r,y,ph = 1728*y/r^4 \n", "Riem(g)^ph_y,r,ph = 1728*y/r^4 \n", "Riem(g)^ph_y,y,ph = 24*(r^2 - 72*y^2 - 12*r + 72)/(r^3*y^2 - r^3) " ] }, "execution_count": 27, "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": 28, "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()\n", "print(Ric)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us check that the Curzon-Chazy metric is a solution of the vacuum Einstein equation:

" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = 0$ " ], "text/plain": [ "Ric(g) = 0" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Weyl conformal curvature tensor is

" ] }, { "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()\n", "print(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us exhibit two of its components $C^0_{\\ \\, 123}$ and $C^0_{\\ \\, 101}$:

" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C[0,1,2,3]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{24 \\, {\\left(r^{2} - 72 \\, y^{2} - 12 \\, r + 72\\right)}}{r^{5}}$ " ], "text/plain": [ "24*(r^2 - 72*y^2 - 12*r + 72)/r^5" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C[0,1,0,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

To form the Mars-Simon tensor, we need the fully covariant (type-(0,4) tensor) form of the Weyl tensor (i.e. $C_{\\alpha\\beta\\mu\\nu} = g_{\\alpha\\sigma} C^\\sigma_{\\ \\, \\beta\\mu\\nu}$); we get it by lowering the first index with the metric:

" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,4) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "Cd = C.down(g)\n", "print(Cd)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The (monoterm) symmetries of this tensor are those inherited from the Weyl tensor, i.e. the antisymmetry on the last two indices (position 2 and 3, the first index being at position 0):

" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetry: (2, 3)\n" ] } ], "source": [ "Cd.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Actually, Cd is also antisymmetric with respect to the first two indices (positions 0 and 1), as we can check:

" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Cd == Cd.antisymmetrize(0,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

To take this symmetry into account explicitely, we set

" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "Cd = Cd.antisymmetrize(0,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Hence we have now

" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetries: [(0, 1), (2, 3)]\n" ] } ], "source": [ "Cd.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Simon-Mars tensor

\n", "

The Simon-Mars tensor with respect to the Killing vector $\\xi$ is a rank-3 tensor introduced by Marc Mars in 1999 (Class. Quantum Grav. 16, 2507). It has the remarkable property to vanish identically if, and only if, the spacetime $(\\mathcal{M},g)$ is locally isometric to a Kerr spacetime.

\n", "

Let us evaluate the Simon-Mars tensor by following the formulas given in Mars' article. The starting point is the self-dual complex 2-form associated with the Killing 2-form $F$, i.e. the object $\\mathcal{F} := F + i \\, {}^* F$, where ${}^*F$ is the Hodge dual of $F$:

" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form FF on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathcal{F} = \\frac{12 \\, e^{\\left(-\\frac{24}{r}\\right)}}{r^{2}} \\mathrm{d} t\\wedge \\mathrm{d} r -12 i \\mathrm{d} y\\wedge \\mathrm{d} {\\phi}$ " ], "text/plain": [ "FF = 12*e^(-24/r)/r^2 dt/\\dr - 12*I dy/\\dph" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "FF = F + I * F.hodge_dual(g)\n", "FF.set_name('FF', r'\\mathcal{F}')\n", "print(FF) ; FF.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us check that $\\mathcal{F}$ is self-dual, i.e. that it obeys ${}^* \\mathcal{F} = -i \\mathcal{F}$:

" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "FF.hodge_dual(g) == - I * FF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us form the right self-dual of the Weyl tensor as follows

\n", "

$$\\mathcal{C}_{\\alpha\\beta\\mu\\nu} = C_{\\alpha\\beta\\mu\\nu} + \\frac{i}{2} \\epsilon^{\\rho\\sigma}_{\\ \\ \\ \\mu\\nu} \\, C_{\\alpha\\beta\\rho\\sigma}$$

\n", "

where $\\epsilon^{\\rho\\sigma}_{\\ \\ \\ \\mu\\nu}$ is associated to the Levi-Civita tensor $\\epsilon_{\\rho\\sigma\\mu\\nu}$ and is obtained by

" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (2,2) on the 4-dimensional Lorentzian manifold M\n", "no symmetry; antisymmetries: [(0, 1), (2, 3)]\n" ] } ], "source": [ "eps = g.volume_form(2) # 2 = the first 2 indices are contravariant\n", "print(eps)\n", "eps.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The right self-dual Weyl tensor is then:

" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field CC of type (0,4) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "CC = Cd + I/2*( eps['^rs_..']*Cd['_..rs'] )\n", "CC.set_name('CC', r'\\mathcal{C}') ; print(CC)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetries: [(0, 1), (2, 3)]\n" ] } ], "source": [ "CC.symmetries()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{24 i \\, r^{2} - 1728 i \\, y^{2} - 288 i \\, r + 1728 i}{r^{3}}$ " ], "text/plain": [ "(24*I*r^2 - 1728*I*y^2 - 288*I*r + 1728*I)/r^3" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CC[0,1,2,3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ernst 1-form $\\sigma_\\alpha = 2 \\mathcal{F}_{\\mu\\alpha} \\, \\xi^\\mu$ (0 = contraction on the first index of $\\mathcal{F}$):

" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "sigma = 2*FF.contract(0, xi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Instead of invoking the function contract(), we could have used the index notation to denote the contraction:

" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma == 2*( FF['_ma']*xi['^m'] )" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form sigma on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sigma = \\frac{24 \\, e^{\\left(-\\frac{24}{r}\\right)}}{r^{2}} \\mathrm{d} r$ " ], "text/plain": [ "sigma = 24*e^(-24/r)/r^2 dr" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma.set_name('sigma', r'\\sigma')\n", "print(sigma) ; sigma.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The symmetric bilinear form $\\gamma = \\lambda \\, g + \\underline{\\xi}\\otimes\\underline{\\xi}$:

" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms gamma on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\gamma = e^{\\left(\\frac{144 \\, y^{2}}{r^{2}} - \\frac{144}{r^{2}}\\right)} \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{r^{2} e^{\\left(\\frac{144 \\, y^{2}}{r^{2}}\\right)}}{y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} - e^{\\left(\\frac{144}{r^{2}}\\right)}} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y + \\left( -r^{2} y^{2} + r^{2} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "gamma = e^(144*y^2/r^2 - 144/r^2) dr*dr - r^2*e^(144*y^2/r^2)/(y^2*e^(144/r^2) - e^(144/r^2)) dy*dy + (-r^2*y^2 + r^2) dph*dph" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gamma = lamb*g + xi_form * xi_form\n", "gamma.set_name('gamma', r'\\gamma')\n", "print(gamma) ; gamma.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Final computation leading to the Simon-Mars tensor:

\n", "

The first part of the Simon-Mars tensor is

\n", "

$$ S^{(1)}_{\\alpha\\beta\\gamma} = 4 \\mathcal{C}_{\\mu\\alpha\\nu\\beta} \\, \\xi^\\mu \\, \\xi^\\nu \\, \\sigma_\\gamma$$

" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,3) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "S1 = 4*( CC.contract(0,xi).contract(1,xi) ) * sigma\n", "print(S1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The second part is the tensor

\n", "

$$ S^{(2)}_{\\alpha\\beta\\gamma} = - \\gamma_{\\alpha\\beta} \\, \\mathcal{C}_{\\rho\\gamma\\mu\\nu} \\, \\xi^\\rho \\, \\mathcal{F}^{\\mu\\nu}$$

\n", "

which we compute by using the index notation to denote the contractions:

" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,3) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "FFuu = FF.up(g)\n", "xiCC = CC['_.r..']*xi['^r']\n", "S2 = gamma * ( xiCC['_.mn']*FFuu['^mn'] )\n", "print(S2)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "S2.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Mars-Simon tensor with respect to $\\xi$ is obtained by antisymmetrizing $S^{(1)}$ and $S^{(2)}$ on their last two indices and adding them:

\n", "

$$ S_{\\alpha\\beta\\gamma} = S^{(1)}_{\\alpha[\\beta\\gamma]} + S^{(2)}_{\\alpha[\\beta\\gamma]}$$

\n", "\n", "

We use the index notation for the antisymmetrization:

" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "S1A = S1['_a[bc]']\n", "S2A = S2['_a[bc]']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

An equivalent writing would have been (the last two indices being in position 1 and 2):

" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "# S1A = S1.antisymmetrize(1,2)\n", "# S2A = S2.antisymmetrize(1,2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Simon-Mars tensor is

" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field S of type (0,3) on the 4-dimensional Lorentzian manifold M\n", "no symmetry; antisymmetry: (1, 2)\n" ] } ], "source": [ "S = S1A + S2A\n", "S.set_name('S') ; print(S)\n", "S.symmetries()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}S = \\frac{41472 \\, y e^{\\left(-\\frac{48}{r}\\right)}}{r^{6}} \\mathrm{d} r\\otimes \\mathrm{d} r\\otimes \\mathrm{d} y -\\frac{41472 \\, y e^{\\left(-\\frac{48}{r}\\right)}}{r^{6}} \\mathrm{d} r\\otimes \\mathrm{d} y\\otimes \\mathrm{d} r -\\frac{41472 \\, e^{\\left(-\\frac{48}{r}\\right)}}{r^{5}} \\mathrm{d} y\\otimes \\mathrm{d} r\\otimes \\mathrm{d} y + \\frac{41472 \\, e^{\\left(-\\frac{48}{r}\\right)}}{r^{5}} \\mathrm{d} y\\otimes \\mathrm{d} y\\otimes \\mathrm{d} r + \\frac{41472 \\, {\\left(y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - 2 \\, y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{5}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} r\\otimes \\mathrm{d} {\\phi} -\\frac{41472 \\, {\\left(y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} - y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{4}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} y\\otimes \\mathrm{d} {\\phi} -\\frac{41472 \\, {\\left(y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - 2 \\, y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{5}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\\otimes \\mathrm{d} r + \\frac{41472 \\, {\\left(y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} - y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{4}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\\otimes \\mathrm{d} y$ " ], "text/plain": [ "S = 41472*y*e^(-48/r)/r^6 dr*dr*dy - 41472*y*e^(-48/r)/r^6 dr*dy*dr - 41472*e^(-48/r)/r^5 dy*dr*dy + 41472*e^(-48/r)/r^5 dy*dy*dr + 41472*(y^4*e^(144/r^2) - 2*y^2*e^(144/r^2) + e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^5 dph*dr*dph - 41472*(y^3*e^(144/r^2) - y*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^4 dph*dy*dph - 41472*(y^4*e^(144/r^2) - 2*y^2*e^(144/r^2) + e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^5 dph*dph*dr + 41472*(y^3*e^(144/r^2) - y*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^4 dph*dph*dy" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.display()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} S_{ \\, r \\, r \\, y }^{ \\phantom{\\, r}\\phantom{\\, r}\\phantom{\\, y} } & = & \\frac{41472 \\, y e^{\\left(-\\frac{48}{r}\\right)}}{r^{6}} \\\\ S_{ \\, r \\, y \\, r }^{ \\phantom{\\, r}\\phantom{\\, y}\\phantom{\\, r} } & = & -\\frac{41472 \\, y e^{\\left(-\\frac{48}{r}\\right)}}{r^{6}} \\\\ S_{ \\, y \\, r \\, y }^{ \\phantom{\\, y}\\phantom{\\, r}\\phantom{\\, y} } & = & -\\frac{41472 \\, e^{\\left(-\\frac{48}{r}\\right)}}{r^{5}} \\\\ S_{ \\, y \\, y \\, r }^{ \\phantom{\\, y}\\phantom{\\, y}\\phantom{\\, r} } & = & \\frac{41472 \\, e^{\\left(-\\frac{48}{r}\\right)}}{r^{5}} \\\\ S_{ \\, {\\phi} \\, r \\, {\\phi} }^{ \\phantom{\\, {\\phi}}\\phantom{\\, r}\\phantom{\\, {\\phi}} } & = & \\frac{41472 \\, {\\left(y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - 2 \\, y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{5}} \\\\ S_{ \\, {\\phi} \\, y \\, {\\phi} }^{ \\phantom{\\, {\\phi}}\\phantom{\\, y}\\phantom{\\, {\\phi}} } & = & -\\frac{41472 \\, {\\left(y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} - y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{4}} \\\\ S_{ \\, {\\phi} \\, {\\phi} \\, r }^{ \\phantom{\\, {\\phi}}\\phantom{\\, {\\phi}}\\phantom{\\, r} } & = & -\\frac{41472 \\, {\\left(y^{4} e^{\\left(\\frac{144}{r^{2}}\\right)} - 2 \\, y^{2} e^{\\left(\\frac{144}{r^{2}}\\right)} + e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{5}} \\\\ S_{ \\, {\\phi} \\, {\\phi} \\, y }^{ \\phantom{\\, {\\phi}}\\phantom{\\, {\\phi}}\\phantom{\\, y} } & = & \\frac{41472 \\, {\\left(y^{3} e^{\\left(\\frac{144}{r^{2}}\\right)} - y e^{\\left(\\frac{144}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{144 \\, y^{2}}{r^{2}} - \\frac{48}{r}\\right)}}{r^{4}} \\end{array}$ " ], "text/plain": [ "S_r,r,y = 41472*y*e^(-48/r)/r^6 \n", "S_r,y,r = -41472*y*e^(-48/r)/r^6 \n", "S_y,r,y = -41472*e^(-48/r)/r^5 \n", "S_y,y,r = 41472*e^(-48/r)/r^5 \n", "S_ph,r,ph = 41472*(y^4*e^(144/r^2) - 2*y^2*e^(144/r^2) + e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^5 \n", "S_ph,y,ph = -41472*(y^3*e^(144/r^2) - y*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^4 \n", "S_ph,ph,r = -41472*(y^4*e^(144/r^2) - 2*y^2*e^(144/r^2) + e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^5 \n", "S_ph,ph,y = 41472*(y^3*e^(144/r^2) - y*e^(144/r^2))*e^(-144*y^2/r^2 - 48/r)/r^4 " ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.display_comp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Hence the Simon-Mars tensor is not zero: the Curzon-Chazy spacetime is not locally isomorphic to the Kerr spacetime.

\n", "

Computation of the Simon-Mars scalars

\n", "

First we form the \"square\" of the Simon-Mars tensor:

" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (3,0) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "Su = S.up(g)\n", "print(Su)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "SS = S['_ijk']*Su['^ijk']\n", "print(SS)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathcal{M} & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, y, {\\phi}\\right) & \\longmapsto & -\\frac{6879707136 \\, {\\left(y^{2} e^{\\left(\\frac{432}{r^{2}}\\right)} - e^{\\left(\\frac{432}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{432 \\, y^{2}}{r^{2}} - \\frac{168}{r}\\right)}}{r^{14}} \\end{array}$ " ], "text/plain": [ "M --> R\n", "(t, r, y, ph) |--> -6879707136*(y^2*e^(432/r^2) - e^(432/r^2))*e^(-432*y^2/r^2 - 168/r)/r^14" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "SS.display()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "SSE=SS.expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Then we take the real and imaginary part of this compex scalar field. Because this spacetime is spherically symmetric, we expect that the imaginary part vanishes.

" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{6879707136 \\, {\\left(y^{2} e^{\\left(\\frac{432}{r^{2}}\\right)} - e^{\\left(\\frac{432}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{432 \\, y^{2}}{r^{2}} - \\frac{168}{r}\\right)}}{r^{14}}$ " ], "text/plain": [ "-6879707136*(y^2*e^(432/r^2) - e^(432/r^2))*e^(-432*y^2/r^2 - 168/r)/r^14" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "SS1 = real(SSE) ; SS1" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "SS2 = imag(SSE) ; SS2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Furthermore we scale those scalars by the ADM mass of the Curzon-Chazy spacetime, which corresponds to $m$:

" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{20542695432781824 \\, {\\left(y^{2} e^{\\left(\\frac{432}{r^{2}}\\right)} - e^{\\left(\\frac{432}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{432 \\, y^{2}}{r^{2}} - \\frac{168}{r}\\right)}}{r^{14}}$ " ], "text/plain": [ "-20542695432781824*(y^2*e^(432/r^2) - e^(432/r^2))*e^(-432*y^2/r^2 - 168/r)/r^14" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "SS1ad = m^6*SS1 ; SS1ad" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

And we take the log of this quantity

" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\log\\left(-\\frac{20542695432781824 \\, {\\left(y^{2} e^{\\left(\\frac{432}{r^{2}}\\right)} - e^{\\left(\\frac{432}{r^{2}}\\right)}\\right)} e^{\\left(-\\frac{432 \\, y^{2}}{r^{2}} - \\frac{168}{r}\\right)}}{r^{14}}\\right)}{\\log\\left(10\\right)}$ " ], "text/plain": [ "log(-20542695432781824*(y^2*e^(432/r^2) - e^(432/r^2))*e^(-432*y^2/r^2 - 168/r)/r^14)/log(10)" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lSS1ad = log(SS1ad,10) ; lSS1ad" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Then we plot the value of this quantity as a function of $\\rho = x = r \\sqrt{1-y^2}$ and $z = r y$, thereby producing Figure 10 of arXiv:1412.6542:

" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\log\\left(\\frac{20542695432781824 \\, x^{2} e^{\\left(-\\frac{432 \\, z^{2}}{x^{4} + 2 \\, x^{2} z^{2} + z^{4}} - \\frac{168}{\\sqrt{x^{2} + z^{2}}} + \\frac{432}{x^{2} + z^{2}}\\right)}}{x^{16} + 8 \\, x^{14} z^{2} + 28 \\, x^{12} z^{4} + 56 \\, x^{10} z^{6} + 70 \\, x^{8} z^{8} + 56 \\, x^{6} z^{10} + 28 \\, x^{4} z^{12} + 8 \\, x^{2} z^{14} + z^{16}}\\right)}{\\log\\left(10\\right)}$ " ], "text/plain": [ "log(20542695432781824*x^2*e^(-432*z^2/(x^4 + 2*x^2*z^2 + z^4) - 168/sqrt(x^2 + z^2) + 432/(x^2 + z^2))/(x^16 + 8*x^14*z^2 + 28*x^12*z^4 + 56*x^10*z^6 + 70*x^8*z^8 + 56*x^6*z^10 + 28*x^4*z^12 + 8*x^2*z^14 + z^16))/log(10)" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x z')\n", "lSS1xzad = lSS1ad.subs(r=sqrt(x^2+z^2), \n", " y = z/sqrt(x^2+z^2)).simplify_full()\n", "lSS1xzad" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S1CC1 = contour_plot(lSS1xzad, (x,-20,20), (z,-20,20), plot_points=200, \n", " fill=False, cmap='hsv', linewidths=1, \n", " contours=(-14,-13.5,-13,-12.5,-12,-11.5,-11,\n", " -10.5,-10,-9.5,-9,-8.5,-8,-7.5,-7,\n", " -6.5,-6,-5.5,-5,-4.5,-4,-3.5,-3,-2.5,\n", " -2,-1.5,-1,-0.5,0), \n", " colorbar=True, colorbar_spacing='uniform', \n", " colorbar_format='%1.f', \n", " axes_labels=(r\"$\\rho\\,\\left[M\\right]$\", \n", " r\"$z\\,\\left[M\\right]$\"), \n", " fontsize=14)\n", "S1CC1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "viewer3D = 'tachyon' # must be 'threejs', 'jmol', 'tachyon' or None (default)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics3d Object" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot3d(lSS1xzad, (x,0.12,20), (z,0.12,20), viewer=viewer3D, \n", " aspect_ratio=[1,1,0.05], plot_points=100,\n", " axes_labels=['rho', 'z', 'log(beta)'])" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.3", "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": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 1 }