{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Simon-Mars tensor in Curzon-Chazy spacetime\n", "\n", "This worksheet 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](http://sagemanifolds.obspm.fr) project (version 1.1, as included in SageMath 8.1).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.1/SM_Simon-Mars_Curzon-Chazy.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": { "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 8.1, Release Date: 2017-12-07'" ] }, "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": [ "## Spacetime manifold\n", "\n", "We declare the Curzon-Chazy spacetime as a 4-dimensional manifold:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional differentiable manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M', latex_name=r'\\mathcal{M}')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "m = 12" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

Let us introduce the spacetime metric $g$ and set its components in the coordinate frame associated with Weyl-Papapetrou coordinates:

" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "g = M.lorentzian_metric('g')\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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

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

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

Let us consider the first vector field of this frame:

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

The 1-form associated to it by metric duality is

" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form xi_form on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "source": [ "

Its covariant derivative is

" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(xi_form) of type (0,2) on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "source": [ "

Let us check that the Killing equation is satisfied:

" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form F on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "source": [ "

We check that

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

The squared norm of the Killing vector is

" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field lambda on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

Curvature

\n", "

The Riemann curvature tensor associated with $g$ is

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

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

" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

The Ricci tensor:

" ] }, { "cell_type": "code", "execution_count": 28, "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" ] } ], "source": [ "Ric = g.ricci()\n", "print(Ric)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

The Weyl conformal curvature tensor is

" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field C(g) of type (1,3) on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "C = g.weyl()\n", "print(C)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,4) on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "Cd = C.down(g)\n", "print(Cd)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetry: (2, 3)\n" ] } ], "source": [ "Cd.symmetries()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

To take this symmetry into account explicitely, we set

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

Hence we have now

" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetries: [(0, 1), (2, 3)]\n" ] } ], "source": [ "Cd.symmetries()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form FF on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (2,2) on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "source": [ "

The right self-dual Weyl tensor is then:

" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field CC of type (0,4) on the 4-dimensional differentiable 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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "sigma = 2*FF.contract(0, xi)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form sigma on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms gamma on the 4-dimensional differentiable 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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,3) on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "S1 = 4*( CC.contract(0,xi).contract(1,xi) ) * sigma\n", "print(S1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (0,3) on the 4-dimensional differentiable 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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "S2.symmetries()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "S1A = S1['_a[bc]']\n", "S2A = S2['_a[bc]']" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "

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

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

The Simon-Mars tensor is

" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field S of type (0,3) on the 4-dimensional differentiable 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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (3,0) on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "Su = S.up(g)\n", "print(Su)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "SS = S['_ijk']*Su['^ijk']\n", "print(SS)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "SSE=SS.expr()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "

And we take the log of this quantity

" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "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": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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JTdQnbYwFOOiHwlwvWkefLoR78kW40D/i5I2xxL8J1cLzCfBADMT667X1g/Nh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"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": { "deletable": true, "editable": true }, "source": [ "We also a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "viewer3D = 'tachyon' # must be 'threejs', 'jmol', 'tachyon' or None (default)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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QCpHGzswll3xlwoQrGYZNnCwtRNPV5tff/e6822+/RPGhtra2yZMnu1wurF5H\nDIL56tzTwfMVZ89+sH//WQAUdytAymDWr3+FZW2f+9x8hrENDLw5Onrs0093j44edzovrKwkTZ4V\ny2AAsmh6PobJk0/++skn4bvfvVUu8cRe/6d/+icshkEMhVkzd0hJ3n/zG/jpT7cwDLtr13yKUSGF\n09//0bp1v+vv/4jnJwCAfL40HB4+e/aDY8f+CABlZRdeeOEXAMDpTKhsSa/puQp6luOnTn03HB66\n6qrLMFu3EtbwZMBKmfuMGRCLhcrLL6MdCJI/XV1/2LXrwIEDn7EsLwiVMmOdTJkyglAxaVL9pEkN\nIyNHjx374//8zzaeL7/wwi9MmDA1jaarF3QGQMx6PMPA4OB7R478Phw+d/AgTJo084c/vE/1KRAT\n4Pf7rSHuJs7cU2e058/vGx4+EokMY/JuOvr7PyLVjRznIAUwsuYBEC9zFKW5U8LRo384e/b9cHgI\nAM4/v37SpAaeL1ct6FnUXPHD4oMPtoyMHAGAysppU6bcwPPl5P6ZM90/+cmXVP6yiJEJBAIOh4N2\nFBpgYnFPZf78vjNn/swwHIq7iejq+sO6db9jGM5mczIMS5YjQTxbTypdl5Dn6YOD75886R0ZOcrz\n5ZWV084/v0HSXCVyU3OJI0d+f+JELwBMmjSzsnJakhdEmDnzGpR4xCCYWNxTrbHf/AYef/w/otGR\nnTubaUWFqIeYMAcPHiFLTIkJI5U2yuoas5a+MAAwOPje0aO/J1n85z630Om8MPW5ieOoiZEJh8+d\nOOEdHHwvHB7i+fIpU26orJyW9Wnf/e6tbW0XqzkBYii8Xm9DQwPtKLTBxOIOKc5MNArf+taeQOD4\n7t2LKEaFZGXXrgP33uvhOAfH2eOrkOSynlwAk07QUzl50js4+D5xTiZNaqisnFZWNp5iZxR0hcdO\nnOg9cuT3AOB0XlhZOW3SpNys2E2bVlx7bU7PQChjjeVLBHOL+7PPPtvW1ia/p7m57+RJL89XoDNj\nTLq6/rBu3X/wvEsUYyxrYxhbSldekOusmrWmqfdHIkMnTniJi3LZZTfzfEU8kVczFADAiRO9g4Pv\nEavnyitvy+jzZIYBgD/84c58n47oimUMdzB7tczhw4eT7uE4wWZzUQkGycCxY4NdXX/o6vqTzeYQ\nhAoAhmWFdA4MwzCiKCbKutqKdfIkni+fMuX6ysppR4688dFHLwOA0zmFeOVZQx0cfI88BQAmTWqY\nMuWGjIerqrH5whc2ffe7t86ceREm8gbHMsoOZs/cFW33TZt+HY2GsIOYQTh2bHD58p+FEaM/AAAg\nAElEQVQfOzZoszlZlmcYDsYmS8l8KSQZ62l688pJXayU7uQMAITD544c+f3g4HsA4HRemEHiw+Gh\njz763cjIUQC47LKb44epkm/1YBZvWKxkuIPZxR2U+hAsXOg7ebKvoaEG+xDQ5dixwXXrfrdnz2GW\ntZM+X7Jm6+QQRknTIY2SKmTomY+RMzj43sjIkRMnvADgdF545ZW3yR8Nh4cGB987cuQNAJgy5YZc\nvfU8QIk3IBbYoEOOuW0ZAHC7Fba0F8Xo/v0fYB8CWni97x848OmGDTs5zmGzOQEYIu5xWU9wYGTP\ny6LpuQq6nMrKaaQy/aOPXh4ZOXLgwI+dzimTJjU4nVOOHHmD5PWTJs10Oi+srLxKzYAF8oUvbGIY\n5pZb/mbmzGu+9CW7DmdEsmKBrfXkmD5zT53dXrjQNzj4LgCzY8e3aEVVsuzadeDeezcHAsft9vPs\n9onx6kZWZqyrTNWlw1JPkrdDMvbEcPgcEfRYLBSLhW02V3zWVJs9mPLo9Pud73yrre0iTc6O5A3a\nMsYi9ZvUb34Dv/zlnkDgJNruetLf/9G9924eGBjiOHs0GhgZOTJxYo28wJEcllHTMyfpOSmmqoM/\n/PC3J070Tp3aqmaiNfkERejVvnHj/4czrohWsNkPMRvf+hY4nVMYhu3qGqYdS0lw7NhgQ8PKb3/7\n6dOngefLOc5ht09kWT4aDcYb8445MInLTZNUnmEYkC7y+1OXpyrB5HLwGIJQJQhVGZSdSY/KU+TE\nihU/v/76n19//c+LMTiSme7ubtohaIzpxb21tbW3tzf1fodj0q9+tUP/eEqKXbsO3Hjjw1//+gae\nr+C4MobhWNYWbyHAjIwchbEuMckb4MVh5LKeen/Gk+ej5oqQFU+6Kbgarr/+53ff/Rqts5cmFjPc\nwQITqumw2coiEeuUrBqK/v6PAICYMDZbGceVSYIuCaLDMSkSGUldlCTdTFFOlUpaqODKJfvs2fcY\nBijpeJYz9vb++frr/wwAv//93+sST6nT3Gy1niVWEPd0LTpjsZD+wVie/v6Pli9/nOPsHOfg+XJZ\nTxiQNw9gGCYcPhsKDQpCVfypqXOkegh6BuGeNGnmkSOvF7D6NO05NRzr+usfB5T44mOlqVSC6SdU\nIc2K4YULfWfPvj9jxuWPPlpHJSqL0d//UVfXH3ftOsCyvM3mjJerS+0bk+oaGQA4c8bvdF4kCJUp\nsq7GQM+ZPLLvEyd6jxx5fcaMf8z1VNoua1LPd7/7reXLFbpRIkgqpvfcM1BWdsGBAx/TjsIKdHX9\nYfnyx1977X1BmMDzrnhPGE7uxqS46gzL8kNDH5JHiPuRzR/P2UAv0B8fHHw38/BpLkBF2QHgySd/\nc/31j999914qZ7cwXq+XdgjaYwVxdzgcP/jBD1Lv5/lyUYzqH49lOHZs8N57N99448M//vFeQajk\nODvL8gxjA2AlZSfzpakKyDDgdJKetxkkO+dJUW0nPJ3OiwAgHB5KL+IGhOnt/fP11z+BEq8h27Zt\nox2C9ljBcweAEydOJN1TWzvl0KHPOM5+8CBMn04lKBPT3//RunUv9/d/zPMuhrFxnD1rV95USz0W\nC7OsEIkMp7Ryyy03z/u3SB0s6XY4fE67wfOgoF9NmnGdOfPqH/+4UZuIShXLtPmVYwXPHdLY7vPn\n94+MfBaNhnbsuIVKVGaEeOu7dx/iuDKW5QGAZW1xjU3aGkmCYRgQRQVLfXT0OM+7SAcClQFopOaq\nBvnggxdGRj6bMeP/1+KM+QSgIRs33oELoPLD6/W63W4r9YMkWCRz9/v9qZPdweApu31iIHCSSkim\n49ixwXXrXt6928dxAs9PYBgmcWuktLKeeCUBhoHR0eMVFVdkPrWegi4n38y96MJNXg/Z52V27rrr\nCQB44407ihaUlbGesoNlxF2xjMlmKwNgRDGmfzzmor//o7a2JxiGY1me510sy8NYQxiQyXo6+yWd\nmQ4AIAhVw8OfKZ60MEHXRl6zibuWIp745UbtU3LlhhueIFdQ5dWjmBpaACtMqBJS57v/1//6XDQa\ndDov+NrXfk0lJONDsvW2tl/abE6eL7fZnCwrkMlSGF9cyspKRMabBKTMOipORTIAEAqdGbuR51xo\nsaY6J02alWb8nM8i752geIG8xDrradNdbrjhFzfc8Iv+fs3PaEF8Ph/tEIqCRTJ3RW65ZfKbb74L\nACyLLVUVWL78iQMHPrHZnIIwAYBhWQ4AJF2LZ+4Qvzl+PYW0osVxgt1eFQqdsdsn5hhdMayP1AnV\noRxndzUNJ3HsYgx6112/AICf/ex7aMdnoKamhnYIRcE64p7a2L2mBuz2quHhz+KyhQCMmTC/AGAS\nZV1eAzPuwKRfTZpFjKRn2myu4eFPK7I009Vc2vIcUGv5NkQ9JZH473znluXLUzeSRaCpqYl2CEXB\nOraMw+FI7eu2ZEltNBqMxSKbN4epRGUourr+eNNNj9x++1M8XyEIE1jWRi5krWniIiPJPEnyKNJa\nFukq0EkdZCyW+vpraLPk5qhIJonTOQUg2Twp7LxFsY804amnfku8GtqBGAuv12vJ2VSwkrhDmq9X\nPF8ejQafeea3+sdjHHbtOjhzZvtjj+08fZrh+XKWtbEsT3Y0TVqFJFPn1FRdWa0ye+g87wKAaFTq\n81O48OWgoXK/O9X+PnFiH9H3NGdRPJdBtVs9N9zwi7vvfp12FEbBes0gJSwl7qnLzG65Bez2iSQ5\npRISdY4dG7zppkd/+MMtPF9B+nzJNF2qh5GUHVJkS1nIcpkaZVyuS0ZGPs1XEHOW8tRMPF2MlZVX\nj4wcSS/cZpTvrF8mGADG6333hht+ecMNv8QZVwtjHc8dANrb21Pv5DgHx5UFg59u3hxZvNhSv28G\njh0b7Or604EDHx048JnNVsbzFQxjkyz1pD4wSpOlaZN01SGMHxmLhcLhnDZOyX6WPCoLVY5MG10j\nvOuuX5Irb7zxd3qe1zhY1XAHi+Wz6RpE8Hy5y3XJU0/16BwPLbq6/tjW9ovNm9/y+wd5vpxhbCzL\ny1rBkNJGNtGBSXIhxskpSVccweW6BABGRwfUPVHR0M+jsjC7kTIyolyDrymqUmnqVg9J5GmdnRYW\nNtzBYuLe2tqaWu3+4otX22xlsViE46xfEElk/bHHdp06FbXZXCzLsSwv3x0JQN7EMdV+SaAQQU+C\nNJlJ86x03xJymuekpZIGFev8uOGGXz733LHnnjtGOxCdsLDhDhazZQDA5/OlLjbjOIfN5rD2UtX+\n/o/Wr3/lwIHPOM5Odp9gWRsAyJcgKdU1KqbJaiQpN9my2ydGIlmKylV7LIxW7dQnT5792Wd71Z2x\nVHjqqd8CwFNPwc9+9ndYHW9qrCbuilx77eV9fZFo9NMvfvG5115bTjsc7bnppkePHx8mq0xZlpN1\n+GIgQawzaTpkl/X8NI4BAJ53jY4eC4VOC8L4aqZc1FyTSJL57LO98Q4EFpdvhmFEUZR+Svcr3kn4\n/vefBICGhqs2bLhB11h1JHVxjJWwSFfIrNx225/PnfvL8PCnr7/+bdqxaMaxY4M33fQj2dZITGJj\nXojLdaaZ0iLk6coHnzixr6rqGpvNpdpmKRLjI3/22WuDg++63YZrw6Jpo2MNaGi4esOG62lHgeRG\nCYl7IHAiFgtdeunIpk1fpx1OofT3f/yDH7x44kQgXtfIxXe8S8rWC5H1XPUli+Vy5syfY7HQeefN\n0O6Masg0pt//BM9XTJ3aUoTzKoViMMnOg9df/y7tEBC1WGpCNTMOxyRRFH2+42EzL1Y9dmxw1qzV\n3/nOs6dPixzn4DhBXgkTnwRlE2fzlAtg0pwhp5lA6SMky6QoALhcl8iWMiWdS5O5x5znM3m+Qqv9\nOsa+ImVEkxPRZe7cJ+fOfdIa1fGKldNWwoLirvg3O3FinyjGWNZm3mnV/v6PZ81affPN6202p83m\nlC1HYlJknaAgcCpkXSWMTNkTH0hT5UKWqmqn5hrUpVRVXa1e3LMKtzXkWw3f//6Tc+c++dxzGWpb\nEfpY0Jbxer2pBTP/9/96//u/Y6IYCQROnTq1/7/+64dUYsuPXbsOdne/efDgZyzLc5wdgGEYDsZN\nmFRlyaMGJidZTx1c1fFnzhy22Vzl5ZeqPleW8xaIoi1TOhqdDakqSfqpDHo1xsSCmbviDPhddzWI\nYgSA4XmXuT7PHn+8/4c/fMnvP8nz5RxXxjC2eN06l7gQCVJzWLlXkGZ4NWmv8uAAyhl6hpFtNldi\ntXtmtDVtUkZnmKqqqyElJdf8RNqh6DsV7wIpP5Uvc+c+NXfuU+ZK5AOBAO0Qio4FxV1xyVl/P4yM\nHIlGg6IYO//8+v/8TxP47m+9FZk1a82zz74iCBUsK7Asz7Jk4pSYMPINkhTsl6QrKahUzEzeS64j\n2+3nhcPDsVhI8dFiqHlWB1yXRarKoSVqqEq1NS5PP/1vc+c+dc89v6cdiCqsvXyJYEFxByXb/ZZb\ngOcn8Hy5KMZsNsf/+T+PUwlMJZEIzJq15q67HhGESoaxkWwdAMibPLOsgyxhTzO8GqVQFpT0qboq\nDeJ5F8fx0Wg48VkqQ8oBlWl4OHyOJO9ak5NSG121c8LrfXfu3KdoR5GddK1KrERJLGIiuFyXMAwT\niQwPD3/qcl1MO5y0zJq1hmE4QagEADJfSt7/Mu8FEq8kULC3nj4hV9b03GBZYXj446oquXVWkLoV\nYqSEQudGRj67/PLcTqjV+lgLQ/S9oeHqDRu+QDsWZZqbm2mHUHQsOKGajttuO8yyfDB4OhoNDg19\nePXVEzZt+gbtoBL43vde9Hrf4zgHsdTlTnrKWqTUm5lljjyUVZXSfWCoPTLr4KOjx4aGPp48eXbu\nTyeRaKmqPt/jAFBT8/eKp9LwRCXO669/h3YIpYg1bRnF2ZIZMy4/d+5Du/08AGBZ/s9/Pqt7XGl5\n/PEDc+as7e//yGZzkt2RGIYBYKUpU6WprXFUSJ4oe7paMpowOQwjD5hsphqJDKmOoYiznTxfkRih\naQzuFJJ8HmNd5s59eu7cp6m9Nimkthe0JNYUd4fDkWq7L11aFgyeBgCWtblcl0Qio9///qs0okvg\nrbeis2c/8Mwzv7PZXFIHRwAmqT9M5tRbsTdIImrcmKQPjHTHqBQ+5YNZVuB518hIlr6DRatdSRAd\n2ctLHfkfOo8LpHvBjQOReCMsgCqF2VQoKc/dZgOX62JRjNls5aHQGZutzOs9DPC3FEOaPfsBjnPY\nbGVklSkkeOuQ+EaVUu+89T0dyc8qLFXPfiTLChwnpJxUW1VK+0LJCYXOCUKWrbu1iKRIBxcRshdK\nMfj+958GgJ/+9NvYcrLYWFbcU6vdN28Gu70qFBq026siEaGi4q9GRt7MazcfDZg9+36W5Ymsx1NI\nApNfSEya3n5Zn5cyTvZjVA6VDqfzwtOn/S7XpUUQ9NzicbkuKqz9AIV/Hd3+XYt6on/4h6cB4Pbb\nv1FfX11XV8QTKdLSolM3IbpY05YBpdnwxYuBYWw2W5koRu32KgCorJzW2Kh32db3vrd1zpy1NlsZ\nx5WxrCDbn1rK3KVjU3MnMc39GTJ3tV/Vlex1lc/NzQ3g+XKGgVxWM2U4aZI1UQwymyEFjJuyvZSa\ni5V45pl/v/vupxsbdbXjLd9SRsKy4p66lOmf//k4xwmiGBVFiERGWVbg+QpRjOgW0ltvxebMWdvf\n/yHPl7OsnWU5mawTRAAQRfk3YjHNsm/135kzHJlBKrSXdbmNbrefFw6rnVNNPJeWUh4OnwuF5Jm7\nZgpueJlO+tXyM/oVTX9IGRnSv4xj9zc2Pt3Y+LQ+a1xramp0OIsRsKy4A4DH45HfnDFjMsvaASAc\nPiuKUYZhAURBqLrnnj/oEMz3vrd1xYp/IVvfkRoYAIhbw4SErFySeFEEJYlnUu8URTGXwtaE91ui\n1mgm6+kKXVhWiMWyLhIuamLOADCh0DmX66I8TqGjcBcuuxk+sTR8bZnEK0min+4XSbj/mWd+19j4\nzP79WoSDWFvcfT6f/ObixcCyHADEYmGbzQUALMvb7RP37/8gGCxiGN/73kuzZz/Q3/8X0soxruzk\nP5tM+sUSlVq6Kcr0HRKPkc+vjpPGmcmk+IlilPWtrlYOMte62O0TR0ePZhxfQ4HMlI8PD6dtP1A0\n7c4gdmnjLB3uvvuZxsZnaEdhBSw7oQopc6qbN4Moiiwr8Hy5zeYQxSgABAInAJivf/3F3btv0zyA\nSATuvPOlvr734iUZY9WNoigCSBY5sWJE8k0i/lSp0mNMxGWzrPIikGTVVnLeUwVCpuW5JeyqND3r\nMQDA8+UkeWdZXuXIqslhqHD43OTJs7VOtDU8rHSR9H3v3tu1HblEZlPB2pl7a2ur/Ob06QAAZPPo\naDTI8y6GYR2OSUQu33jjuIan/vRT8Y47tl133dr+/r9wnJ0sR4rr+FhDeVGMiXHkN+NjJOXp8gfl\nmp410daELFlkHmXpZWUXnj7t0yI/zSHVTUrABSGnzTow0aZAY6OWiXyJLF8iWFncIXFm/OBBAACb\nrQwAotEgANjtE202Z3n5ZSzLr1r1kobnvfXWB/v63rfZXPEN8GIAMZKwA4iiGAUgEh8TxXETRsri\nZUIu/8lIRk2S7ucyv6qYtmcQJlWyrvrsULAO5qCnauwUpa6QKNyGg0h84XZ8iSxfIlhc3FMQRRE4\nrgxAJBk0x5UJQmU0GozFInfe+e+Fn+Dxxw/NmdPJcXZSwE7kO36JimKUSHz8ppSzx4iqp6p8okWT\nNG0FSTdTdFZZ9FN89nRoJesKEul0XhiLhVTUzGgp5UmkaT9gfFT69ea9gOIfgtjxzz2X/5dsxc0e\nrIrFG4cFAgGpJvI//gM2bx4AYEQxOjo6wHECw7CiKAYCJ2y2sqGhj4aGPg6FBt9+O/8y2Dvu2Ob1\nvhv3kRPMcZkbLqXhkiInfMTKb5IIE1fJMym6nPA2SBTcdJ8BCncqHqlILql6piPPnn2f58vLyi7M\n9YnxMFRHkWZAn2/T5MlzJk+ek9NAWsNgm8k8qK+ftmHD/871WYrbtFmVEsrciS3DMAxZ+x6LRTjO\nIYoxu71qdHSA5ysmTPhcXJdzJhKBOXM6+/rejzdeJ3l3VBQjsVg4FosQN0YUozJvnRgyMSlzl54o\nDUuUPZ6/JzH+yTF+VybBU6nsmbJX1dm6qiw4Gg0FAqdSnqLwxBxLVtIlg8mEQufOnPmzil8nP6SP\n3nyyVCQzfX3vNTY+29j4rHqvxuPxlI6yg+XF3eFwSB0iyYRq3I0RRDEWi4UFYQIAU1Z2YTg8FA4P\nlZdfescdOXfxf+ut2F//9QMcZyc3Y7FwLBYWxXDce4mJYjQWi0i2jGTCiGIsnrhB/CbELSMxfj2p\nACb1u1Y6aUhO4VVUPRYo66o0XaKi4vJIZDgWC2c8b9YMXZWOK1JwYxlUbfrcffez99zzRzVHlpQn\nA5YXd5BNoZDMHQBEEQShCgBisQgAkHaMLtfFglAZiYweOPDxt7/9K/XjP/74obvu+leOsxNNj0RG\nAYiaR2OxcDQalFQ+FouKYkxexg5jHzZj15M6zJArslPl1LZX4TDZmDkk7CpkPVdVHTveZisHAJZN\naCKmLj3PR8rzJbN8I/RRmcWXwu5Lcqwv7tJf9MABaXFzjBS5k5yRZW0cJ3CcneMcFRVX2GzOw4dP\nffvbz6oZ/K23Yk89tV0UY6IYiUYDsVhYFCORSCAcHorFwrFYSBTFWGzMjSFpeCw2lrzLpk+lqMRE\noU8yahR9lXHStJMEpbRdLepkPfsw6TSR58uDwVM5qrlmqhoKncvY0t0KCp70F2QKI48RFMMoEnff\n/Wxj47PpZlxLYfclORafUJUTn1AlM5bs8PAnACAIEwAAQAyFzkYiw+HwCMMw5879Tyg0ODz8aX//\n+gwD/vzn/U8//Rvinsdi4VgsGi9zBIYhznuMZflYLMpxAnFXGMYGIJKNlgAAgCHTp/FJVPJmYOLv\nBSauy3L3FuIPQfxOAMiu7GkeVbwnaUDlxzM+mv0wMnwgcOrs2ferqz+f7/i5kjCsz7fJ6bzoiitu\nLc65CoKJt/ksoJmzNSGSxTBZtOv227++fPlkvYIyIiUh7lLNzLJlY8k7w9jC4XOk/S/DcJHICIAY\niYwEAieCwUFBqBgZORIInHC7Jz/99DLFMWtq/l4QqmKxIMvao9EgqVsnU6MsayMrThmGYxiOZTny\n/QDinysMw8S7t0vizpD740tVGZmgQ1zxQSa5CZZuBmXPVvKocGdGKcnJe0kdOfmeaDR08mSfTNy1\nVbEso7333vMAMG3aUk1PmhZUairU10977LG/kRfOlQjWt2UgoUPk+Nof2X4RjM3mZBie48rs9vPK\nyiZFowEAEISq/fs/mDVrzd69nyYNeOWVC4LBk+fOfTA8/MnQ0F+i0dFweDgcHibOTDQaihe3SUuW\nSHmM5KSP2d/x77msTKaJ1sdvyb7YylA5WSf/JFBlsqc5XYZBFI9JPjKD5UJmoQOBU1p4IDk7KsPD\nyX/Zgk6vztPQ8IyIGvr63vviF5/7znfuoR2I3pSEuEvrVB966ALJ1CbzeKIYI3kxx9mJ7S4IlYJQ\nVVHxObt9ost1sd0+8R//8Wf19T9Yt24XGeTKKxfIBxfFaDB4MhweikYDRNbjCRqQXu0MI7WBlKRT\n3hUSyCeBdE8GNZcZMgnyn3gYyIwdUNI4zWU9k6ArjZqgv+XllwWDp1IPUoEG5rjLdbHak6kzlxED\n8tpry7/+9RtoR6E3JSHuElIPYFJ0yPPl0jLRaHSUXA+HhxiGDYfPMgwnCJU8P6Gy8iqbzdnd/brb\n/XdXXbWUYWwpasIwzNjELDHTk1x1yWmJy73ckJH3iWRlVnuCM5NO2aUAZA8lmexJqJd1NaKp+DmR\nXdDl8HxFMHgqGg1lPFHSCIWn+WOcOXM44Ryo3ZbjtdeWA0BTUxPtQPSmJDx3OcuWHQMAhuEAmFBo\nMBoNkLJIUYzGYiFSkB4KnRHFWCQSCIfPAjCjo0djsWg0GojFQtFoMBg8HYuFRDFGfjIMyzA2hmFZ\nVhDFCMsKks/OMBzL2sgVouyJKbz8uuTPQPx6krInp+dpEnbyEKQ8BKlqmDFVz4yCoOc7FMRioRMn\nvBMn1pKebjk9txAYhunr+9eLLvpbpelcE2GxTx3lXtZ5Q5S9NLFyy185SdMpZF7LZisj9joAMAzH\nsnayT5MgVIXD53ie4zh7KDRYVnZBJDISjQZCobM8X8Gytnh1YzQaDUprx2OxsM1WwTCsKMZYlmdZ\nmyjGyJwqjOXy0kypNIkqKXuCiyLJ/VhoKWKdKP3yJyYfqfjmz1fWFYfKdZBkSBPmPJ6oksxJd2F7\nqGqIxTQ6bzL936pj/FNBUnaPx1M6nX4lSsWWkardFy++IL63EbCsEF/6DwAgiuFYLMwwTDQaikZD\nohiNRgOktJFsdkp22+D5Cp53cZyD58vJT7u9ymZzOhyTbDYnx9nJqiiGYTnOzrI2kr+T9pDxEhom\nfp2VGTXSdWl+lZHtsCpl94yissfNkCTLIlcTJh0Jj6b30/NzSxierzh9+lDuT1QaK0c7pZjiLjfK\nsl4QrWAAmPr6q+Q5e9K+PSVCqWTuEjNmAIxl7gAADsf50WiIbJTBMBxAJBaLsKxNECZEo0GbjbXZ\nnJHIaDQ6CgA2mxiNBiKRUZblOa4sGh0lG21Ho6H4dqw8jE3SQry0MUaKIJVqHMkVKYsH6f5c6h0V\n8nrFm4Vn62kGyEfNk27b7eeNjBzJeRQtKgvji5jyI2f/CtGBtrably+fJL+ndPZNlVMq4i41Ibjk\nEuk+EYBhWSEcHpb2AyKOOYAYDg8DiBzHh0KDkcgIwwDH2WOxEMNwdvvEQOCkzeaw2Rzh8DAAkN6N\nLFsmihHim4tilFjt8eYwrCRBsqaPqU56UqaZn6yr9NZz0PrCvZfMTyEFkeHwUIrtnhSG+mkDDUGB\nNhMbNiyrq6MdhDEoFXHv7OxMukdK3qWbAMAwbDQaIEY8w3CxWJhlBbtdiEaDRNlJhwBBqIxGAwzD\n8Xw5gEi2/ojFwixrJz57vGO7GPdVQLLmU+Q7rYKn03QYV9tMqXrKudIelv7pqQfk2pxW1cEsK7Cs\nMDJypLJyWmIARRfWuC1TOgrOpExayv8/Rdn9SQ9B4vXUI5M2CKNQqfHaa8pLDkvQcIfS8dwBQGoP\nKa92ByCVM9JNkeMcxCtnWZ5cSOdeMoNKckyOE2w2J5ksFUWRZXmWFWw2JxEpMirL2jiOlxnrNul6\n3F5nZc7w+ILVpHvk5gzxkOWdCeIPJfu2aezmdPau/DMm1U9PDiMb+VjJDsf54fC5nOzy3El2unm+\nwum82AzKnpN9n/kCSlfkp4DEg0F2BZSOZ1Kuaxht6phpSafsHqkCusQoIXGX5lQvvRRA1jmX58vl\n9aAMw0SjQdLBMd6KHVjWbrOVk82VGMYWi0UYhmEYjuMcUm07AEPmUVlWkCogWZZPnEodU/b4rqrJ\nJfDp3h5kSVSaR8cjV5LFDFKbcH9hE6T5CLo8ZqdzCqk0zenpqkNSDiwcPkejWkZ7XSsNMn1mpFN2\nKNXZVCgdW0aJMUGPxcLyRD4aDZBlq6IYJWIdi3GxWFA6jON4juOj0TDLkqbBDMsK8SbsY41l4suR\nRFGMsSwrigAQk/bIlgXAAMjNh7HP2kSRVcybZHfl5r0kP1SAn56/3KTGTFYIB4OnnM4puQ6WdxgA\nEA6fLeTpWoVRPNJ9/xHFDKsTikK85QZovrTmtdd06g5kLkpuERPhkUfgwIGj0q5J0WiQlDwCQDB4\nRhSj4fA5jnNAfOcN0iKGZPHRaJD0ZwcAADEWCyfWU5LdOUhXA4jvuJQq6+RgAJBslgzt2gvX9JSc\nXCFJV0nOkqDSYDl37sNg8OSkSTM1DyAdfX3/UlV1zRVXzFN3uK5aiEtiU1H8eLWgX1wAACAASURB\nVEBlT0cJ2TJy7r0XIN6EIIloNEDmSLdv/3y8yN0GwBJlJ6WN8e4CoihGGYZjGBvL2ph4FzBpYarM\nmZHcFbm1Ilko5H2c8FDSt/L05duZnQcF4yW9n56OLOaG8nNyt87TlMpkd1fyQ8mQyfTFP+8TMUw+\nFyQV6ZWRXqWsyi7NtJUgpSXuUgcxQqLVTqrRo+RnKHQWAH796+sAIBYLi2KUYWxExKW9kxiGYxie\n1MiLoiiz1Bmp329c2qSpVMlel8+gji9fin9CpJPy8Xizqbn0qZCkF+oFK2dRK3AulOcrotFgODxU\nDClPgeH5CQBQVeVOPFc+ZzSSTKf7ZDLORRtefXXpq69mz9mlGugSpLTEPYVxnx0AGIaNRAIAEAqd\n27VrbNOWJUv+d1yCmfgSVqn0hcyjAsva4qk6ETguLvQAwCQ1cJcydLnEy8VFXgiv4h2SSc1zzNAh\nzSkyPqEwQZefkePsPF+Rx2qmbOOD4gtI3PakxmHJT05JFYsp30mfMTSls5ho8AnR1vZ1lScrtX1T\n5ZSWuMv/0g89dCHEk3diuZBXg+McsVhYOmzBAvi3f2uMxUKxWIQk4KIoxhP8WHzJUiy+0ZKk6ZLK\nS8bL2FVZhj7+EHmG7M3JKr1Rld/M2dQ883s+N2lQ8ZUi+xgZzuhwnB8InMx9zNRhk15YBUjmTlr+\nZlbtguU7V102hUZT49VXlyxbdp7Kg3t6eooajJEpLXFvbW1NvVMURUGolG4pPnHZsq8SpSaLmOJJ\nN6mQGcvBpe2nScvJ+Ft0vOVAvAJSOkySZjKCXDrjHwXjnwoKOp7ebNFMzcdj1SI3z3pG0gxAXXli\nnhmr9LqRs4RCZwvTbmtk06bh1VeX5HR8aS5fIpSWuANAd3c3uXLppSCvgCTJOOkq/vLLX0t61m23\nwY9+9GWS4DMMG9/wmpFJsKT4INW9yPRQfo1NtGgymTBJEp+XfDCJg6uisPQ8f2nj+QqOE8LhofSj\nqf+SocpCiW+iq/J3QeGmSa7KXuKUnLgntRCKdx0Yc89HR49GIiOKT3S7oa7uc6QIUtYCTJT6FoBs\nX6f4k4goy833cdNGNrZaJyENGYZSNVrBZouWekemVTUX8XQkTqiidhuXPJS9ZNemEkpO3OU8//wU\nKXOPREYBwG7P5OX9679e88or35BeNFGMxTfcGJd40k84SSIlG4fcIqoha/abRFKurSZ5zMOdKJZv\nXthQDM9XBIMnYzGFpaoFiHjqCzX2TG23UdURxd/IAhdl8svZS3k2FUpQ3BsaGhLvIHtYR8LhQQAx\nHD5ns5VlHqGu7q9INSTZl4PsfE0kHmBs69S4fDNJm18nWivxuxOazORtbSeQ4Acpket4Gql59jcz\nacIcfwHzK0pJdxaFIShVlBeuy/JxrETyb1pff1XebkzKm720KDlxB5ntLsEwNtLwi+PsV1+d2YSF\nhx+uXb/+Vvky1HjmzpDXU5pZhfFS+vE3YaKaMIrXFYVYUaAVr8tvqnlBlNBEzdXmZSDTcVIQGQic\nUBF7btlfEsRtL0LmrlKarafL2lNfP239+jw3QfR6vdoGYzpKUdzlTJ8+hegvmVCNxcIPPvhXWZ9V\nWwv19VNhfI2rJKPEnIF4Ip+qsAzJqmUpvHQ/pJOndDKd6PzkJxYF6WO20TIemj4rF4TUDTQ0DHIM\nUi1DCiJzQWVOjRTKhg2teSs7yBoFliylKO7Nzc3S9ZYWAIhJzjvp6KuGRx65dv36pvj7WZRl6IwY\nd+Clt3pcyiVIZk1ETVEO0n0Hz0M7iqdEqkbLY8LT6bzo3Lm/0FNM1G76bNjQeu21BY1Q4oY7lKa4\nyz/SSftfAGAYWywWCgYH1Y8zfTq0td0IEIPxxFmMX0/Y7kAu/bL7JYnPKh+pT1R/0QS1I+c+4akw\nMsfZBaFiePgzjYJXPi/PTwBgXK6LUb4lUr//aTIDlCuvvlqoskNiDlealKK4J/3Vp0+fAgA2mzMW\ni4ZCZ3IaqrXVtWvXAkhsU5OYtqeaM2klPnFFUup13ciu43kVIOb22TMyUri4Z/rMI+0HDF4tI02f\nQPy/qKiknkWf88p59dVWTUoYHQ5H4YOYmlIUd4fDIZ9smTEDAESWtUWjo4JQlceARN8l4jKXoYVv\n0v3jMpey6DTpejG8lHykPK+z5IDdPin7QZnOlf2MpDecdv3c1ZKT0kGivlub+vppe/a0AEBLS0sw\nGAwG89+5JbVoogQpRXGHRGfm5psBgCGrT9etuymP0To6OpYsYeRd2uPJewKJ70/FzUgTJJ4cLp80\nlV3J+5IJHfJxlXCcXWlXJi3P5XJdEh9TG9TrNZJ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"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 8.1", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 0 }