{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Schwarzschild horizon in 3+1 Eddington-Finkelstein coordinates\n",
"\n",
"\n",
"This Jupyter/SageMath worksheet is relative to the lectures\n",
"[Geometry and physics of black holes](http://luth.obspm.fr/~luthier/gourgoulhon/bh16/)\n",
" \n",
"These computations are based on [SageManifolds](http://sagemanifolds.obspm.fr) (v0.9)\n",
"\n",
"The worksheet file (ipynb format) can be downloaded from [here](https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/Schwarzschild_horizon.ipynb). To run it, you must start SageMath with the Jupyter notebook, with the command `sage -n jupyter`\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we set up the notebook to display mathematical objects using LaTeX formatting:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%display latex"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Spacetime\n",
"\n",
"We declare the spacetime manifold $M$:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4-dimensional differentiable manifold M\n"
]
}
],
"source": [
"M = Manifold(4, 'M')\n",
"print M"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and the 3+1 Eddington-Finkelstein coordinates $(t,r,\\theta,\\phi)$ as a chart on $M$:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Chart (M, (t, r, th, ph))"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X. = M.chart(r't r:(0,+oo) th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n",
"X"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The mass parameter and the metric:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"var('m', domain='real')\n",
"assume(m>=0)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"g = (2*m/r - 1) dt*dt + 2*m/r dt*dr + 2*m/r dr*dt + (2*m/r + 1) dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g = M.lorentzian_metric('g')\n",
"g[0,0] = -(1-2*m/r)\n",
"g[0,1] = 2*m/r\n",
"g[1,1] = 1+2*m/r\n",
"g[2,2] = r^2\n",
"g[3,3] = (r*sin(th))^2\n",
"g.display()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"[ 2*m/r - 1 2*m/r 0 0]\n",
"[ 2*m/r 2*m/r + 1 0 0]\n",
"[ 0 0 r^2 0]\n",
"[ 0 0 0 r^2*sin(th)^2]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g[:]"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"[ -(2*m + r)/r 2*m/r 0 0]\n",
"[ 2*m/r -(2*m - r)/r 0 0]\n",
"[ 0 0 r^(-2) 0]\n",
"[ 0 0 0 1/(r^2*sin(th)^2)]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g.inverse()[:]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Gam^t_t,t = 2*m^2/r^3 \n",
"Gam^t_t,r = (2*m^2 + m*r)/r^3 \n",
"Gam^t_r,r = 2*(m^2 + m*r)/r^3 \n",
"Gam^t_th,th = -2*m \n",
"Gam^t_ph,ph = -2*m*sin(th)^2 \n",
"Gam^r_t,t = -(2*m^2 - m*r)/r^3 \n",
"Gam^r_t,r = -2*m^2/r^3 \n",
"Gam^r_r,r = -(2*m^2 + m*r)/r^3 \n",
"Gam^r_th,th = 2*m - r \n",
"Gam^r_ph,ph = (2*m - r)*sin(th)^2 \n",
"Gam^th_r,th = 1/r \n",
"Gam^th_ph,ph = -cos(th)*sin(th) \n",
"Gam^ph_r,ph = 1/r \n",
"Gam^ph_th,ph = cos(th)/sin(th) "
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g.christoffel_symbols_display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us check that we have a solution of Einstein equation in vacuum: "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Ric(g) = 0"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g.ricci().display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The scalar field $u$ defining the horizon"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"u: M --> R\n",
" (t, r, th, ph) |--> -1/2*(r/m - 2)*e^(1/4*(r - t)/m)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u = M.scalar_field(coord_expression={X: (1-r/(2*m))*exp((r-t)/(4*m))}, name='u')\n",
"u.display() "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAJJCAYAAACwH6CqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nohgQREQkigFBRESi/h9x+dfnpfrkAQAAAABJRU5ErkJggg==\n",
"text/plain": [
"Graphics object consisting of 10 graphics primitives"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plm2 = implicit_plot(u.expr().subs(m=1)+2, (r, 0, 15), (t, -10, 15), color='green') + \\\n",
" text('$u=-2$', (11,12), color='green')\n",
"plm1 = implicit_plot(u.expr().subs(m=1)+1, (r, 0, 15), (t, -10, 15), color='green') + \\\n",
" text('$u=-1$', (6.3,12), color='green')\n",
"pl0 = implicit_plot(u.expr().subs(m=1), (r, 0, 15), (t, -10, 15), color='green') + \\\n",
" text('$u=0$', (3.1, 12), color='green') \n",
"pl1 = implicit_plot(u.expr().subs(m=1)-1, (r, 0, 15), (t, -10, 15), color='green') + \\\n",
" text('$u=1$', (0.8, 0.5), color='green') \n",
"pl2 = implicit_plot(u.expr().subs(m=1)-2, (r, 0, 15), (t, -10, 15), color='green') + \\\n",
" text('$u=2$', (-0.2, -2.5), color='green', background_color='white') \n",
"graph = plm2+plm1+pl0+pl1+pl2\n",
"show(graph, aspect_ratio=True, axes_labels=[r'$r/m$', r'$t/m$'],)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"graph.save('def_Schwarz_Hu.pdf', aspect_ratio=True, axes_labels=[r'$r/m$', r'$t/m$'])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1-form du on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"du = -1/8*(2*m - r)*e^(1/4*r/m - 1/4*t/m)/m^2 dt - 1/8*(2*m + r)*e^(1/4*r/m - 1/4*t/m)/m^2 dr"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"du = u.differential()\n",
"print du\n",
"du.display()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Vector field on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"-1/8*(2*m + r)*e^(1/4*r/m - 1/4*t/m)/m^2 d/dt + 1/8*(2*m - r)*e^(1/4*r/m - 1/4*t/m)/m^2 d/dr"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"grad_u = du.up(g)\n",
"print grad_u\n",
"grad_u.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us check that each hypersurface $u={\\rm const}$ is a null hypersurface:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"0"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g(grad_u, grad_u).expr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The null normal $\\ell$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Scalar field on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"M --> R\n",
"(t, r, th, ph) |--> 1/4*(12*m*log(2) - 4*m*log(2*m + r) + 8*m*log(m) - r + t)/m"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rho = - log(-grad_u[[0]])\n",
"print rho\n",
"rho.display()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Vector field l on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"l = d/dt - (2*m - r)/(2*m + r) d/dr"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"l = - exp(rho) * grad_u\n",
"l.set_name('l', latex_name=r'\\ell')\n",
"print l\n",
"l.display()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAJGCAYAAABCyGGmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQqFQKBSKMqCKJ4VCoVAoFIoy8H8oDGezC6Hi6AAAAABJRU5ErkJggg==\n",
"text/plain": [
"Graphics object consisting of 81 graphics primitives"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"graph_l = l.plot(ambient_coords=(r,t), ranges={r:(0.01,8), t:(0,8)}, fixed_coords={th:pi/2, ph:pi}, \n",
" parameters={m:1}, color='green', scale=0.8, aspect_ratio=1)\n",
"show(graph_l)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us check that $\\ell$ is a null vector everywhere:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"0"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g(l,l).expr()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1-form lf on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"lf = (2*m - r)/(2*m + r) dt + dr"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"l_form = l.down(g)\n",
"l_form.set_name('lf', latex_name=r'\\underline{\\ell}')\n",
"print l_form\n",
"l_form.display()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"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"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"Levi-Civita connection nabla_g associated with the Lorentzian metric g on the 4-dimensional differentiable manifold M"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nab = g.connection()\n",
"print nab\n",
"nab"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"nabla_g(lf) = (2*m^2 - m*r)/(2*m*r^2 + r^3) dt*dt + (4*m^3 + 4*m^2*r - 3*m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) dt*dr + m/r^2 dr*dt + (2*m^2 + 3*m*r)/(2*m*r^2 + r^3) dr*dr - (2*m*r - r^2)/(2*m + r) dth*dth - (2*m*r - r^2)*sin(th)^2/(2*m + r) dph*dph"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nab_l_form = nab(l_form)\n",
"nab_l_form.display()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"(2*m^2 - m*r)/(2*m*r^2 + r^3) dt*dt + (4*m^3 + 4*m^2*r - m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) dt*dr + (4*m^3 + 4*m^2*r - m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) dr*dt + (2*m^2 + 3*m*r)/(2*m*r^2 + r^3) dr*dr - (2*m*r - r^2)/(2*m + r) dth*dth - (2*m*r - r^2)*sin(th)^2/(2*m + r) dph*dph"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nab_l_form.symmetrize().display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check of the identity $\\ell^\\mu \\nabla_\\alpha \\ell_\\mu=0$:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"0"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = l.contract(nab_l_form, 0)\n",
"v.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The null normal as a pregeodesic vector field"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"[ m/r^2 (2*m^2 + 3*m*r)/(2*m*r^2 + r^3) 0 0]\n",
"[ -(2*m^2 - m*r)/(2*m*r^2 + r^3) -(4*m^3 + 4*m^2*r - 3*m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) 0 0]\n",
"[ 0 0 -(2*m - r)/(2*m*r + r^2) 0]\n",
"[ 0 0 0 -(2*m - r)/(2*m*r + r^2)]"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nab_l = nab(l)\n",
"nab_l[:]"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Scalar field on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"M --> R\n",
"(t, r, th, ph) |--> -2*(4*m^2 - 2*m*r - r^2)/(4*m^2*r + 4*m*r^2 + r^3)"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"div_l = nab_l.trace()\n",
"print div_l\n",
"div_l.display()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-2*(4*m^2 - 2*m*r - r^2)/((2*m + r)^2*r)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"div_l.expr().factor()"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/4/m"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"div_l.expr().subs(r=2*m)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Vector field on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"4*m/(4*m^2 + 4*m*r + r^2) d/dt - 4*(2*m^2 - m*r)/(8*m^3 + 12*m^2*r + 6*m*r^2 + r^3) d/dr"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"acc_l = l.contract(0,nab_l,1)\n",
"print acc_l\n",
"acc_l.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The non-affinity parameter $\\kappa$:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"M --> R\n",
"(t, r, th, ph) |--> 4*m/(4*m^2 + 4*m*r + r^2)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kappa = l(rho)\n",
"kappa.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check of the pregeodesic equation $\\nabla_{\\ell} \\ell = \\kappa \\ell$:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"True"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"acc_l == kappa * l"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"4*m/(2*m + r)^2"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kappa.expr().factor()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Value of $\\kappa$ on the horizon:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/4/m"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kappaH = kappa.expr().subs(r=2*m)\n",
"kappaH"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The complementary null vector field $k$"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"k = (m/r + 1/2) d/dt + (-m/r - 1/2) d/dr"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k = M.vector_field(name='k')\n",
"k[0] = 1/2 + m/r\n",
"k[1] = -1/2 - m/r\n",
"k.display()"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"0"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g(k,k).expr()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-1"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g(k,l).expr()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAJGCAYAAACnVqTKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"Graphics object consisting of 153 graphics primitives"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"graph_k = k.plot(ambient_coords=(r,t), ranges={r:(1,8), t:(0,8)}, nb_values={r:8, t:9}, fixed_coords={th:pi/2, ph:pi}, \n",
" parameters={m:1}, color='red', scale=0.8, aspect_ratio=1)\n",
"graph_lk = graph_l+graph_k\n",
"show(graph_lk)\n",
"graph_lk.save('def_plot_lk.pdf')"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"kf = -1/2*(2*m + r)/r dt - 1/2*(2*m + r)/r dr"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k_form = k.down(g)\n",
"k_form.set_name('kf', latex_name=r'\\underline{k}')\n",
"k_form.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The 2-metric $q$\n",
"\n",
"We define $q = g + \\underline{\\ell}\\otimes \\underline{k} + \\underline{k}\\otimes \\underline{\\ell}$:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"q = r^2 dth*dth + r^2*sin(th)^2 dph*dph"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q = g + l_form*k_form + k_form*l_form\n",
"q.set_name('q')\n",
"q.display()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tensor field of type (2,0) on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"r^(-2) d/dth*d/dth + 1/(r^2*sin(th)^2) d/dph*d/dph"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q_up = q.up(g)\n",
"print q_up\n",
"q_up.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Expansion along the null normal"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We compute $\\theta_{(\\ell)}$ as $\\theta_{(\\ell)} = q^{\\mu\\nu}\\nabla_\\mu \\ell_\\nu$:"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-2*(2*m - r)/(2*m*r + r^2)"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta = q_up.contract(0,1,nab(l_form),0,1)\n",
"theta.expr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check of the formula $\\theta_{(\\ell)} = \\nabla\\cdot\\ell - \\kappa$:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"True"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta == div_l - kappa"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check of the forumla $\\theta_{(\\ell)} = \\frac{1}{2} \\mathcal{L}_{\\ell} \\ln \\det q$:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"True"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"detq = M.scalar_field({X: r^4*sin(th)^2})\n",
"theta == 1/2*ln(detq).lie_der(l)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"True"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta == 1/2*l(ln(detq))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Deformation rate tensor of the cross-sections\n",
"\n",
"We compute $\\Theta$ as $\\Theta = \\frac{1}{2} \\mathcal{L}_{\\ell} q$:"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tensor field Theta of type (0,2) on the 4-dimensional differentiable manifold M\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"Theta = -(2*m*r - r^2)/(2*m + r) dth*dth - (2*m*r - r^2)*sin(th)^2/(2*m + r) dph*dph"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Theta = 1/2 * q.lie_der(l)\n",
"Theta.set_name('Theta', latex_name=r'\\Theta')\n",
"print Theta\n",
"Theta.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Expansion of the cross-sections along the null normal $k$:\n",
"\n",
"We compute $\\theta_{(k)}$ as $\\theta_{(k)} = q^{\\mu\\nu}\\nabla_\\mu k_\\nu$:"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-(2*m + r)/r^2"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta_k = q_up.contract(0,1,nab(k_form),0,1)\n",
"theta_k.expr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Value of $\\theta_{(k)}$ at the horizon:"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-1/m"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"theta_k.expr().subs(r=2*m)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 7.4.beta5",
"language": "",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}