{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Radial free fall in Schwarzschild spacetime\n", "\n", "This Jupyter/SageMath worksheet is relative to the lectures\n", "[Geometry and physics of black holes](https://relativite.obspm.fr/blackholes/).\n", "\n", "Click [here](https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/ges_radial_free_fall.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, with the command `sage -n jupyter`\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.1.rc3, Release Date: 2017-11-23'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "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": [ "## Schwarzschild-Droste coordinate $t$ as a function of $\\eta$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "var('eta r0')\n", "assume(eta>0, eta2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The function $\\frac{\\mathrm{d}t}{\\mathrm{d}\\eta}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-1/2*r0*sqrt(1/2*r0 - 1)*(cos(eta) + 1)^2/(4/r0 - cos(eta) - 1)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dtdeta = r0/2*sqrt(r0/2-1)*(1+cos(eta))^2/(1+cos(eta)-4/r0)\n", "dtdeta" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The primitive:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*((r0*sqrt(1/2*r0 - 1)*(2*arctan(sin(eta)/(cos(eta) + 1)) + sin(eta)) + 8*sqrt(1/2*r0 - 1)*arctan(sin(eta)/(cos(eta) + 1)))*sqrt(2*r0 - 4) - 8*sqrt(1/2*r0 - 1)*log(-(sqrt(2*r0 - 4)*(cos(eta) + 1) - 2*sin(eta))/(sqrt(2*r0 - 4)*(cos(eta) + 1) + 2*sin(eta))))/sqrt(2*r0 - 4)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dtdeta.integrate(eta).simplify_full()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Since this is a complicated expression, let us try to find something simpler by taking $u=\\eta/2$ as a variable; we have then $\\frac{\\mathrm{d}t}{\\mathrm{d}u}= 2 \\frac{\\mathrm{d}t}{\\mathrm{d}\\eta}$:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2*r0^2*sqrt(1/2*r0 - 1)*cos(u)^4/(r0*cos(u)^2 - 2)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('u')\n", "assume(u>0, u" ], "text/plain": [ "(sqrt(2*r0 - 4)*r0*sqrt(1/2*r0 - 1)*cos(u)*sin(u) + (r0*sqrt(1/2*r0 - 1) + 4*sqrt(1/2*r0 - 1))*sqrt(2*r0 - 4)*u - 4*sqrt(1/2*r0 - 1)*log(-(sqrt(2*r0 - 4)*cos(u) - 2*sin(u))/(sqrt(2*r0 - 4)*cos(u) + 2*sin(u))))/sqrt(2*r0 - 4)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = dtdu.integrate(u).simplify_full()\n", "t" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We force some obvious simplification by" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*(r0*cos(u)*sin(u) + (r0 + 4)*u)*sqrt(2*r0 - 4) - 2*log(-(sqrt(2*r0 - 4)*cos(u) - 2*sin(u))/(sqrt(2*r0 - 4)*cos(u) + 2*sin(u)))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = (t*sqrt(2*r0-4)/2/sqrt(r0/2-1)).simplify_full()\n", "t" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We note that, given the range of $u$, the argument of the logarithm is negative; let us enforce $\\ln|x|$ as the primitve of $1/x$ instead of $\\ln x$ or $\\ln(-x)$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-(sqrt(2*r0 - 4)*cos(u) - 2*sin(u))/(sqrt(2*r0 - 4)*cos(u) + 2*sin(u))" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = t.operands()[1].operands()[0].operands()[0]\n", "x" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*(r0*cos(u)*sin(u) + (r0 + 4)*u)*sqrt(2*r0 - 4) - 2*log(abs((sqrt(2*r0 - 4)*cos(u) - 2*sin(u))/(sqrt(2*r0 - 4)*cos(u) + 2*sin(u))))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = t.subs({x: abs(x)})\n", "t" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We move back to $\\eta$, with some extra simplification enforced:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*(2*r0*cos(1/2*eta)*sin(1/2*eta) + eta*(r0 + 4))*sqrt(1/2*r0 - 1) - 2*log(abs((sqrt(1/2*r0 - 1)*cos(1/2*eta) - sin(1/2*eta))/(sqrt(1/2*r0 - 1)*cos(1/2*eta) + sin(1/2*eta))))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = t.subs({sqrt(2*r0-4): 2*sqrt(r0/2-1), u: eta/2})\n", "t" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Finally we invoke `trig_reduce()` to let appear $\\sin\\eta$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*(eta + sin(eta))*r0*sqrt(1/2*r0 - 1) + 2*eta*sqrt(1/2*r0 - 1) - 2*log(abs(sqrt(1/2*r0 - 1)*cos(1/2*eta) - sin(1/2*eta))/abs(sqrt(1/2*r0 - 1)*cos(1/2*eta) + sin(1/2*eta)))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = t.trig_reduce().simplify_full()\n", "t" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Plot of $r$ as a function of $\\tau$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*sqrt(1/2)*sqrt(r0^3)*(eta + sin(eta))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tau = sqrt(r0^3/8)*(eta + sin(eta))\n", "tau" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*r0*(cos(eta) + 1)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = r0/2*(1 + cos(eta))\n", "r" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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x9fVl7969nD17lpSUFBYtWsTChQvJy8sjMTGR8PBw+vfvf/VvWDgwrGi46667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\nh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"text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r0_values = [2.1, 3, 4, 5, 6]\n", "graph = Graphics()\n", "for r0_val in r0_values:\n", " tau1 = tau.subs({r0: r0_val})\n", " r1 = r.subs({r0: r0_val})\n", " graph += parametric_plot((tau1, r1), (eta, 0, pi), \n", " color=hue(r0_val/6), thickness=2,\n", " legend_label=\"$r_0 = {:.2f}\\\\; m$\".format(float(r0_val)),\n", " axes_labels=[r'$\\tau/m$', r'$r/m$'])\n", "show(graph, aspect_ratio=1, gridlines=['minor', 'major'])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"ges_radial_infall_tau.pdf\", aspect_ratio=1, \n", " gridlines=['minor', 'major'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Plot of $r$ as a function of $t$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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RFQIwrfdAaPFRFC31WrMGjh6FCxfAJOcWkks62Khec801/PM//zN33XUXPXv2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\niJedRWcRH8FiOrX4rMnP567KSmo8IzWXtbbyy7N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173yCrfkA/AMNteJzmquQxJ12AYB2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\nAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = Graphics()\n", "for r0_val in r0_values:\n", " t1 = t.subs({r0: r0_val})\n", " r1 = r.subs({r0: r0_val})\n", " graph += parametric_plot((r1, t1), (eta, 0, pi), plot_points=300,\n", " color=hue(r0_val/6), thickness=2,\n", " legend_label=\"$r_0 = {:.2f}\\\\; m$\".format(float(r0_val)),\n", " axes_labels=[r'$r/m$', r'$t/m$'])\n", "graph += polygon([(0,0), (2,0), (2,26), (0,26)], color='lightgrey', alpha=0.7)\n", "graph += line([(2,0), (2, 26)], thickness=1.5, color='black')\n", "show(graph, xmin=0, xmax=8, ymin=0, ymax=25,\n", " aspect_ratio=1, legend_loc=(0.8,0.8))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"ges_radial_infall_t.pdf\", xmin=0, xmax=8, ymin=0, ymax=25,\n", " aspect_ratio=1, legend_loc=(0.8,0.8))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Spacetime diagram based on IEF coordinates" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*((eta + sin(eta))*r0 + 4*eta)*sqrt(1/2*r0 - 1) + 4*log(sin(1/2*eta)/sqrt(1/2*r0 - 1) + cos(1/2*eta))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ti = 2*(sqrt(r0/2-1)*(eta + r0/4*(eta + sin(eta))) + \n", " 2*ln(cos(eta/2) + 1/sqrt(r0/2-1)*sin(eta/2)))\n", "ti" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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UiRdCdTU7eIDCpk3JHDgQAHN+PpGvvqpzj4So/mp88ACkjR1LkW1v9+AffiDo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\nImhOqGteD4nwJEht6y9RZ8QIvX3lCoFBZqjBwmMCq5PLgC4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"text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = Graphics()\n", "for r0_val in r0_values:\n", " ti1 = ti.subs({r0: r0_val})\n", " r1 = r.subs({r0: r0_val})\n", " graph += parametric_plot((r1, ti1), (eta, 0, pi), \n", " color=hue(r0_val/6), thickness=2,\n", " legend_label=\"$r_0 = {:.2f}\\\\; m$\".format(float(r0_val)),\n", " axes_labels=[r'$r/m$', r'$\\tilde{t}/m$'])\n", "graph += polygon([(0,0), (2,0), (2,26), (0,26)], color='lightgrey', alpha=0.7)\n", "graph += line([(2,0), (2, 26)], thickness=1.5, color='black')\n", "show(graph, xmin=0, xmax=8, ymin=0, ymax=25,\n", " aspect_ratio=1, legend_loc=(0.8,0.8))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"ges_radial_infall_IEF.pdf\", xmin=0, xmax=8, ymin=0, ymax=25,\n", " aspect_ratio=1, legend_loc=(0.8,0.8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Infall time" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*pi*(r0 + 4)*sqrt(1/2*r0 - 1) - 2*log(1/2*r0 - 1)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tif = 2*(pi*sqrt(r0/2-1)*(r0/4+1) - ln(r0/2-1))\n", "tif" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(r0 + 4)*sqrt(1/2*r0 - 1)*arctan(sqrt(1/2*r0 - 1)) + r0 - 2*log(1/2*r0) - 2" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tih = 2*(2*(1+r0/4)*sqrt(r0/2-1)*atan(sqrt(r0/2-1)) + r0/2-1 -ln(r0/2))\n", "tih" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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81++/Q7t21g3R+cGhfHl47TVYtUrBQcTTtGFaREREfN6RI9YN0S+8AEePusa7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\nrJ2yVpe9BThf7D1/5zMbpjt06EBoaCj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1+PrrmDp1qs+9jt9/h969oWbNBbz+uqMgOJQp\nA/37Q3z8AK6+emqh4BAofx52ex3JyckB8TogMP483P06goKD2DR/U0FwmBU+i7MfPJu7/q+9O4+L\nql7/AP4ZGHYRXFDJBPdcUBQJQRDFlNQSM8tAvblkmeZWXslSb3qzTMtMzSV3M0Urc+nmliui4IYb\nKSiKkqYoCggOO/P74/wER1ABz8x3Zs7n/Xr5usOZYc4z8bkDz3zPc87ufxU3DiJfx4O6lfLz4Osw\nntfRs2fPZ3odVJqsMw9JSUlo1KgRTp06hdatWxc/rnPnzmjbti3mzJlT6jkMPfMQEhKCLVu2wtZW\nusBVq1bAmTN63y0RQkJCyjw7mQgnT0oXdvv1V+DhdwB7e2kG6N//hk6TTabPmPJH+pEan4of2v6A\ntu+0RZfpXWDrbCu6pGLMH4nC7MnPYAPTP/74I958881Sz2Ho5kGj0cDe3h6NGgGXLwPVqknDoUT6\n9iB7Ih08CHz5JbBjh+52Z2dg9GhgzBigJo9uMEvGkD/Sv6ybWahSp4roMkph/kgUZk9+FZ55uH//\nPhITE/Gg57h8+TJOnz6N6tWro169ehg3bhymT5+Oxo0bo379+pgyZQqef/559O7dW/biK+NBgOrW\nlZqHtDTpwlfMFembqDcvrRbYvl1aaXhkRRe1awMffQS8/z5goJOdkSD85akMxtg4AMwficPsya/C\nzcPx48cRFBQElUoFlUqF8ePHAwAGDRqEFStWIDw8HBqNBsOHD0d6ejo6duyI7du3w9raWvbin8XD\nQ9PXrwNNmoirhUgfCguBjRullYbTp3Xvq18fCA+XhqHt7ERUR0QVkZeVh8OzD6PD+A6wrmJcv0+J\nSFme6bAlOYi4zgMg/eH09dfS7b17gaAgg+2aSK/y8oA1a4CZM4GLF3Xva9EC+OQT6VoNVlZi6iOi\n8tNqtUjYkoDtY7bj3t/34DfeD8Hf8KJXRCSOQc62ZEweTOjXq1ey7coVMbWQsjx6dgi53b8PzJ0r\nnVJ12DDdxuHFF4FNm4CzZ4GBA9k4KJG+80fyS0tKw/qQ9djQZwPu/X0PAHB88XFo7mgEV1ZxzB+J\nwuzJT9brPJgCNzc3ALrnrL90SVAxpCgPsie3W7eA77+XLuz26PB/ly7SSsNLL0lXhybl0lf+SH4F\nOQU49PUhRH0ZhYKcguLtjYIboeeCnrCvYXrHcDN/JAqzJz/FHraUkAA0aybdDg0FnnJJCSKjc+kS\nMHs2sHIlkJOje19IiNQ0+PqKqY2IKufe9XtY3Xk17iaWfBJQxbUKun/XHS3ebPHUayYREemb4lYe\nHqhfH7CwAIqKgMRE0dUQld/x48CsWdIwdFFRyXa1GujfX7pGQ6tW4uojospzdHWEQy0H3E28C5Wl\nCr7jfNHps06wcbQRXRoREQAFrzwAQIMG0ryDk5N0ylZ+oEPGSqsFdu6UmoZ9+3Tvq1JFurDbuHG6\nszxEZJpunrqJnR/tRI95PVDLo5bocoiIdChuYPrhy5w/mHvIyOCF4kj/Hs5eeeXnAz/9BHh6Aj16\n6DYOtWtLp2FNTpYOX2LjQE9SmfyRGHXa1MGgvYPMqnFg/kgUZk9+imsewsPDi283blyy/cIFAcWQ\nojycvafJygK++05qcP/1L+ksSQ80aQIsWSKtmn3yiXSVdKKnqUj+SL+0RUIX/IVg/kgUZk9+imse\nvv/+++LbzZuXbI+LE1AMKcrD2XucW7eAyZMBNzfgww+Bv/8uuc/HR5pzOH8eePddwNZWj8WS2SlP\n/ki/CvMLEf1tNBa3WYx8Tb7ocgyK+SNRmD35KW5g+uFTdj08VPrwJ7tE+vCk08UlJpacOSk3V/e+\nV16RLmrYsSPncqjyeLpCsa5GXsW2D7bhVtwtAMDBLw+iy/QugqsyHOaPRGH25Ke45uFhbB5IJK0W\niIoCvv0W2LJF+voBtRoYMEA6c5KHh7gaiejZZKVk4c8Jf+LMmjMlG1VA7r3cx38TEZERU3Tz4OIi\nDZ2mpEjNg1bLT3ZJ//LzgV9+kZqGEyd076tSBRg+HBg7lgPQRKasqKAIxxcfx97Je5GbUdIouLZz\nxSsLX0Fdn7oCqyMiqjzFzTzMnDlT5+sHqw937gA3bwooiBRj6tSZmDVLOkXwgAG6jcNzzwEzZkgz\nDt98w8aB5Pfoex/pV9yGOGwfvb24cbB1tkXPhT0x7MgwRTYOzB+JwuzJT3ErDxqNRufr1q2B3bul\n26dPA66uAoois5aYCMydC/zwgwb5j8xItm0LfPQR0K8fYG0tpj5Shkff+0i/PEI9EPNtDG7E3kCb\nwW3QdWZXONRyEF2WMMwficLsyU/RF4kDgIgI6aq8APDZZ8DUqQYvgczQk+YZVCqgVy+paQgM5KFy\nRObqxskbyNfkw82fA5tEZD4Ut/LwKF/fktsxMeLqIPOQnw/8+qvUNBw/rnufvT0weLA0z9C0qZDy\niMiAXNtyKZuIzI/im4f69UuGpmNigKIiwEJxkyD0rO7eBZYtA+bPB65d073vueeA0aOB994DqlcX\nUx8RySs7LRuZ1zPN6irQRETlobg/k1NTU3W+VqlKVh8yMoCEBAFFkck6e1ZqCp5/Hvj4Y93GoW1b\nYM0aICkJmDgRKCpKffwTEenZo+99VDnaIi1OrjyJ75t+j5/7/oyC3ALRJZkE5o9EYfbkZzTNQ2ho\nKEJCQhAREaHX/QwdOrTUNj+/ktuHD+t192QGCgqA334DgoKkgfulS4HsbOk+lQoICQH275fOpjRw\nYMkgdFnZIzIU5u/Z3Tx1Eys7rsTWoVuhSdXgzoU7iJnD413Lg/kjUZg9+SluYDo2NhZeXl4626Ki\npKv3AtLw9Nq1ei+DTNCdO9KhSQsXAsnJuvc5OgJDhgCjRgFNmpT9/WVlj8hQmL/Ky07Lxt7Je3Fi\n8Qloi0p+Zbbs1xLBs4NR9XnDn+zD1DB/JAqzJz/FNQ9lyc+XjkXPygJq1QJu3ODcA5U4fVqaZVi7\nFsjJ0b3vhRekhmHQIKmBICLzcmbtGewctxOa1JLTPdZoWgM9F/REw64NBVZGRCSG4gemAcDKSjoE\n5fffgVu3gDNngDZtRFdFIhUUAJs3S01DZKTufSoV0LOnNATdrRsbTSJzdv/W/eLGwcrBCoFTAuH3\noR8srS0FV0ZEJAabh/8XHCw1DwCwaxebB6VKSQFWrAAWLZKu9vywqlWBoUOBDz4AGjcWUx8RGZbP\nKB+cXH4StTxqIfgbHqJERKS4z0yXL19e5vbg4JLbW7caqBgyClotcOAAEBoK1KsHfPqpbuPQrBmw\nYIF0JqU5cyrfODwue0SGwPxVjqWVJd6JfgdvrH+DjcMzYP5IFGZPfoprHmJjY8vc3rQp0KKFdPvQ\nIeD6dQMWRUJkZEiHJXl4AJ07Axs2SPMvQMlVoHftAs6dA0aOfPaZhsdlj8gQmL/Ks3G0EV2CyWP+\nSBRmT34cmH7I1KnAtGnS7XnzpGPayfzExkqHJa1bB2g0uvfVrAm884507YaGnIUkMmtZKVnY/fFu\ntBncBvU71xddDhGRSWDz8JC4OKBVK+l2x46lB2XJdGk0wM8/S03D0aOl7w8IAEaMAPr2BWz4ISOR\nWSsqKMLRBUex/z/7kXsvF7U8amH4yeGwUCtuMZ6IqMI4MP2Qli2l49vj44GDB4HERA7Gmrq//pKu\nzbB6NZCWpnufoyPwr38B779f0jQSkXm7cuAKto/ajltxt4q33bt2D7fP3Ubt1rUFVkZEZBrYPDxE\npZLOphMeLn29ZAkwa5bYmqjisrKkVYZly4Do6NL3e3pKqwwDBgBVqhi+PiIyvMx/MrHr37sQFxGn\ns73tO23x0oyX4ODiIKgyIiLTorg12pCQkCfeP3gwYG0t3V65EsjN1X9N9Oy0WuDYMWlWwdVVmlt4\nuHGwsQHefhs4fBg4eRIYPtzwjcPTskekT0rOX0FOAX5o+4NO4/Cc93MYdmQYQpaFsHEwACXnj8Ri\n9uSnuOZh1KhRT7zfxQV4/XXpdmqq9Ak2Ga+7d6UzJrVpA/j4AEuXSisPD7RqJQ2///OPdOiSn5+0\nwiTC07JHpE9Kzp/aVg2fMT4AALsadnh1yat4J+Yd1PWpK7gy5VBy/kgsZk9+HJguw8GDQGCgdLt5\nc2mQmlcRNh5FRcD+/cDy5cDGjaVXh6pUAcLCgHffBby9xTULRGQ8CnIKEDk9En4f+cGuup3ocoiI\nTBabhzJotVLzEBUlff3LL8Abb4itiYALF4AffwTWrAGSk0vf7+cHDBsG9OvHWQYiIiIifWDz8Bg7\ndwLdu0u3W7YETp0C1BwvN7i0NOnibatXAzExpe+vUUOaZXjnHennRETKlHI2BbVb8WxJRET6priD\ncTZv3lyuxwUHS8fQA9LpPpcu1WNRpCM/H/jf/4A33wTq1JHOjPRw42BpCfTsKTUV168D335rGo1D\nebNHpA/mmr+7l+4iIiQCiz0X4/rR66LLoccw1/yR8WP25Ke45iEiIqJcj1OpgDlzSr6ePBm4c0dP\nRRG0WuD4ceCjj4Dnnwd69QJ+/RXIyyt5TOvWwOzZwLVrwB9/SIcnmdIF3cqbPSJ9MLf85WXlYc+k\nPVjYYiEu/H4B0ALbPtiGosIi0aVRGcwtf2Q6mD358bClpxgwAFi3TrodGgowg/I6dw5Yv17675qY\nWPp+FxfpZzBokHRGJSJSNq1Wi7j1cfhzwp/IvJ5ZvL2KaxUEzw6GR6gHVDxLAhGR3rB5eIp//gE8\nPEquThwRITURVHlJSdIhRxERwJkzpe+3tgZCQqRZhu7dASsrw9dIRMYnNSEVvw/7HclRJWdMsLCy\ngN94P3T8tCNsHE1oKZKIyERxBPgpnnsOWLhQOvUnALz/PuDlBTRtKrYuU3PjhnTWqoiIsgefVSqg\nc2fpv3PfvkD16gYvkYiMnIWlhc5cQ9NXmyL422DUaFJDYFVERMrClYdyCguTDq8BgBdekP4AdnYW\nW5Oxu3oV+O036d+hQ9Jcw6Pat5f+2775ptSoERE9yZ5P9+Dcr+fQ/bvuaNKziehyiIgUR3ED00OG\nDKnU9y1ZUnJGn4QE6bCa+/dlLMxMXLgAzJghXZytfn1pADoqSrdxaNUK+PJL4NIlqQkbO1YZjUNl\ns0ckB3PJX+CUQIw4O4KNg4kxl/yR6WH25Ke4w5aCg4Mr9X2OjsDWrdLpW+/cka5C3asX8PvvgIOD\nzEWakMJC4OhR6dSqW7ZIp7UtS/Pm0uFIoaGmcVpVfahs9ojkYC75s7LjEJQpMpf8kelh9uRnNIct\n9ejRA2q1GmFhYQh7MGBghE6cAF56CcjIkL5u105qIFxdxdZlSBkZwK5dUsOwbRuQmlr247y8gNdf\nl/41b27YGonItBTkFODwN4eRm5mLbjO7iS6HiIgew2iaB2OfeXjYkSPSReTu3ZO+fv55YO1aIDBQ\nbF36UlQEnD0L/PknsH07EBkJFBSUfpxKBfj5SSsMffoADRoYvlYiMi1arRYJWxKw86OdSE9Kh8pC\nheGnhvNq0URERkpxhy3JoX17aQD4lVeA5GTpomWdOwMTJwL/+Q9gayu6wmf3999Ss7B7N7BnD3Dr\nVtmPq1JFaqR69QJ69ABq8/c9EZXT7fO3sWPsDlz+83LJRhWQHJXM5oGIyEgpbuUhKioKAQEBsjzX\nzZvSMfwHDpRsa9gQ+Ppr4LXXAAsTGkdPTpYGm6OipGbhwoXHP7ZBA6lZePVVabXFlK7yLJKc2SOq\nKGPKX05GDg5MO4Cj84+iqKDkitANujRA97ndUcujlsDqSB+MKX+kLMye/BTXPISEhGDr1q2yPV9h\nIfDNN8DkybqH8nh4AJ9+Kh3CY20t2+5kUVAgXdn50CGpWTh4UFppeBxHR2llpWtXoFs3oFkz6RAl\nqhi5s0dUEcaUv1/6/YJzv5wr/trJzQnB3waj+evNeXVoM2VM+SNlYfbkp7jmQaPRwN7eXvbnjYsD\nRo8G9u/X3V6jBtC/v3QtAx8fwNJS9l0/UV4eEB8vDXo/+Hf6NJCd/fjvsbQEfH2lRqFrV6luXuX5\n2ekre0TlYUz5uxV3C4vbLIallSX8J/rDf4I/rOz5JmPOjCl/pCzMnvwU1zzok1YrnX1o+vSyr6Jc\nrZp0pqbOnQFPT6B1a0COl1xUJF3B+epVICkJOH9eWlk4fx64eFFaHXkSe3upWQgIkP75+kqrDURE\n+nJq9SnU71wfzu682iYRkSlh86AHWq20ArF0KbBpE5CT8/jHursD9epJZ2yqW1dqJuztATs76X+L\nioDc3JJ/mZnSqVFv35b+959/pEOO8vLKX1+jRtIpZh80DG3acGWBiIiIiJ6OzYOeZWQAGzcCO3ZI\nZy5KSzPcvm1tgRdeAFq0ANq2lRoGLy/AmR/0EZEeJe5IRL0O9WBTlWdTICIyNyZ0PiB5TJgwwaD7\nc3IChg4Ffv5ZWi04cgRYuBAYPlz65L9atWd7/qpVgVatpLMfjRolnelp61YgMRHIygJOnQLWrQMm\nTAC6dGHjIJKhs0f0MEPkLzUhFeteWYe1PdYi8otIve+PTAff/0gUZk9+irvOg5ubm7B9W1pKw8c+\nPrrbNRrg+nXpEKSsLGmYOTtb2m5hIZ0K1dpa+l8HB8DFRfpXo4Z0eBOZBpHZI9Jn/nLSc3Dgv7qn\nXo2ZE4MXR7wI5/r8xIL4/kfiMHvy42FLRERUKUWFRTi5/CT2TtoLTaqmeHvV56ui66yu8Aj14KlX\niYjMjOJWHoiI6Nndv3Ufa4LXIOV0SvE2ta0a/h/7o8OEDrB2MLIL3BARkSzYPBARUYXZu9jDyq7k\nNG0t32qJrjO78tSrRERmTnED0/Hx8aJLIIVi9kgkufOnUqnQfW53uHq5YnDkYLyx/g02DvRYfP8j\nUZg9+SmueQgPDxddAikUs0ci6SN/dX3q4t3j78K9o7vsz03mhe9/JAqzJz/FDUwnJydz8p6EYPZI\npMrkLy8rD9ZVOLtAz47vfyQKsyc/xTUPRET0ZJk3MrH30724cuAKRv41Ume2gYiIlI0D00REBAAo\nyClAzHcxOPjFQeRl5QEAomdHI3ByoODKiIjIWLB5ICJSOK1Wi4QtCdg1fhfSLqcVb7d1toV9TXuB\nlRERkbFR3MD0zJkzRZdACsXskUiPy9+tuFtY020NNvTZUNw4qCxU8B7hjdEXR8P7fW9Dlklmiu9/\nJAqzJz/FrTxoNJqnP4hID5g9Eulx+UuOSkbSnqTir+t3ro/uc7ujduvahiqNFIDvfyQKsyc/DkwT\nESlYUWERlngtQe69XATPDkazPs2gUqlEl0VEREaKzQMRkcKlXU6D43OOUNsqbjGaiIgqyGhmHkJD\nQxESEoKIiAjRpRARKUq1htXYOBARUbkobuUhNTUVNWvW1Pt+iB7F7JGhaVI12PfZPjR9tSmqvViN\n+SNh+P5HojB78jOalQdDGTp0qOgSSKGYPTKUwrxCRH8bjXmN5+H4wuPY+eFODBk8RHRZpGB8/yNR\nmD35KW7lITY2Fl5eXnrfD9GjmD3SN61Wiwu/X8Cu8btwN/Fu8XYrByu0W9wOLw98WWB1pGR8/yNR\nmD35Ka55ICIyRylnUrDzo506p12FCmgzpA26TO8CR1dHccUREZHZ4IQcEZGJy9fkY1XnVchJyyne\n5h7ojpfnvAxXL1eBlRERkblR3MwDEZG5sbK3QsAnAQAA5wbO6LexHwbtH8TGgYiIZKe45mH58uWi\nSyCFYvZIn9qPaY8e83vgg/MfoPnrzUtd6I35I5GYPxKF2ZOf4pqH2NhY0SWQQjF7pE9qGzV8RvlA\nbVP20ajMH4nE/JEozJ78ODBNRGTkMv/JRPyWeLw44kXRpRARkcJxYJqIyEjlZ+cjenY0or6KQv79\nfNTyqAX3ju6iyyIiIgVT3GFLRETGTqvVIm59HBY0W4B9U/Yh/34+AODAtAOCKyMiIqXjygMRkRG5\nduQadn64E9eirxVvU1mq4P2+NzpP7SyuMCIiIihw5SEkJER0CaRQzB49zfEfjmO573KdxqFx98YY\ncWYEen7fE/Y17Sv93MwficT8kSjMnvwUt/IwatQo0SWQQjF79DRNejaB2laNgpwC1GxeE8Gzg9Gk\nRxNZnpv5I5GYPxKF2ZMfz7ZERGREDs06BCt7K7Qb3g6WVpaiyyEiItLB5oGIiIiIiMpFcTMPRESi\npJxJQeaNTNFlEBERVZrimofNmzeLLoEUitlTrswbmdg6bCt+aPsD9k7eK6QG5o9EYv5IFGZPfopr\nHiIiIkSXQArF7ClPviYfBz4/gPlN5uPk8pPQFmlxauUppJxJMXgtzB+JxPyRKMye/DjzQEQkM22R\nFqfXnMbeSXuReb3kMCWbqjboOLkj2o9uD7Wt4k52R0REZoC/vYiIZJSbmYvVnVfjRuyN4m0PLvLW\n6bNOcHBxEFgdERHRs2HzQEQkIxtHGzg+51jcPDTt1RTdZnVDzWY1BVdGRET07IymeQgNDYVarUZY\nWBjCwsJEl0NEVGndvu6GrJQsdP2qKxp0aSC6HCIiItkYzcD0+vXrsXXrVr03DkOGDNHr8xM9MgSG\nNwAAIABJREFUDrOnHDWb1cSwI8OMqnFg/kgk5o9EYfbkZzTNg6EEBweLLoEUitkzD1qtFncv3X3q\n41QqlQGqKT/mj0Ri/kgUZk9+PNsSEVE5/R39N3aN34U7CXcwOnE07KrZiS6JiIjIoBS38kBEVFFp\nSWn49a1fsaLDClyLvobsu9mInB4puiwiIiKDM5qBaSIiY5OTnoPILyJxdN5RFOYVFm+v2bwmGnVr\nJLAyIiIiMRS38hAVFSW6BFIoZs+0nF13FvMazUP0N9HFjYO9iz1eWfQKRpwZgcbdGwuusGKYPxKJ\n+SNRmD35Ka55mDVrlugSSKGYPdOitlMj+242AMDSxhIBnwRgTOIYeL/vDQu16b11Mn8kEvNHojB7\n8lPcwLRGo4G9vb3e90P0KGbPtGi1WqzqtArO7s4Imh4EZ3dn0SU9E+aPRGL+SBRmT36Kax6IiMqr\nMK8QltaWossgIiIyGqa39k5EJIP7t+6jqLDoiY9h40BERKSLzQMRKUre/Twc+PwA5jWahzNrzogu\nh4iIyKQornmYMGGC6BJIoZg9sYoKixC7PBbfN/0e+/+zH3lZedg7eS/ys/NFl2YQzB+JxPyRKMye\n/BR3nQc3NzfRJZBCMXtiaLVaJO5IxO7w3bgVd6t4u8pShRdCXkBhbiGs7KwEVmgYzB+JxPyRKMye\n/DgwTURmK+PvDGwZvAVJe5N0tr/Q+wV0/aorajarKagyIiIi06S4lQciUg676na4ff528dd129dF\nt6+7wb2ju8CqiIiITBebByIyW9YO1gj6bxCiZkThpRkvocWbLaBSqUSXRUREZLIUNzAdHx8vugRS\nKGZPjDZD2mDkuZFo2a+lohsH5o9EYv5IFGZPfoprHsLDw0WXQArF7MlPq9Ui+272Ex9jYWkBtQ0X\nWZk/Eon5I1GYPfnJPjA9bdo0TJs2TWdbs2bNcO7cuTIfb+iB6eTkZE7ekxDMnryS9iVh98e7YWVv\nhUH7Bil6VaE8mD8SifkjUZg9+enl4zgPDw/s2bMHD/oStdp4PvVjgEgUZk8eKWdSsHvibiRuTyze\nduF/F/BCrxcEVmX8mD8SifkjUZg9+enlr3q1Wg0XFxd9PDURKVRGcgb2TdmH02tOAw+tl9ZqVQs2\nVW3EFUZERKQgemkeLl68iLp168LW1hZ+fn6YMWMG6tWrp49dEZEC7Jm0B9Gzo1GYW1i8zcnNCUGf\nB6HVgFawsFTc+BYREZEQsv/G9fX1xapVq7Bz504sXrwYSUlJCAwMxP379+XeVaXMnDlTdAmkUMxe\n5RVkFxQ3DrbVbNHtm24YlTAKnm97snEoJ+aPRGL+SBRmT36y/9Z9+eWX0bdvX3h4eKBbt27Ytm0b\n0tLS8PPPPz/x+0JDQxESEqLzLyIi4onfExERgSFDhpTa/tZbb2Hz5s0623bt2oWQkBBoNBqd7R98\n8AGWL1+usy02NhYhISFITU3V2f7ZZ5+VCmFycjJCQkJKnQps/vz5mDBhgs42jUaDkJAQREVFPfPr\neBRfh/G/jkuXLpnF6xDx8/jpxk9wqO0A/4/9MebSGHQY3wEDBg0wudch8ueh0WjM4nUA5vHzUNrr\nePC719RfxwN8HabzOsr6W7Iir4NKk/1sS2Xx8fFBt27d8MUXX5S6z9BnWyIi01SQUwC1rfGcfIGI\niEiJ9L7en5WVhUuXLsHV1VXfuyIiE5V+Jf2pj2HjQEREJJ7szcOECRMQGRmJq1ev4vDhw+jTpw/U\najXCwsLk3hURmbjUhFRseH0D5jeZj9SE1Kd/AxEREQkle/Nw7do19O/fH82aNUNoaChcXFwQExOD\nGjVqyL2rSnn0ODsiQ2H2SmTeyMTvw3/HwpYLEb8pHkUFRdj76V7RZZk15o9EYv5IFGZPfrI3DxER\nEbh27Rqys7ORnJyMdevWoUGDBnLvptKGDh0qugRSKGYPyMnIwd7JezG/8XzELomFtlAauapSpwoa\nBjeEAUawFIv5I5GYPxKF2ZOfQQamn8TQA9OxsbHw8vLS+36IHqX07CVsTcCWoVuQfSe7eJu1ozX8\nw/3h+6EvrB2sBVZn/pSePxKL+SNRmD35Ka55ICIxbp6+iR/a/gBoAQsrC7w48kV0nNQRDi4Ooksj\nIiKicuLpS4jIIOp41kHrga2hLdQi6PMgVGtYTXRJREREVEFceSAigykqLOIVoYmIiEyY4n6LP3q1\nQyJDMffs3T53GzkZOU98DBsHccw9f2TcmD8ShdmTn+J+k8fGxoougRTKXLOXkZyBLUO2YFGrRTj8\n9WHR5dBjmGv+yDQwfyQKsyc/HrZERJVy//Z9RM2IwrEFx1CYVwgAsLK3wphLY1ClThXB1REREZE+\ncGCaiCokNzMXMXNicPibw8jLzCvebutsC/+J/rCpaiOwOiIiItInNg9EVG5pl9OwzHcZNLc1xdvU\ndmq0H9se/uH+sKtmJ7A6IiIi0jc2D0RUbs4NnOHk5gTNbQ1Ulip4veuFTlM6wfE5R9GlERERkQEo\nbmA6JCREdAmkUOaQPZVKha5fdYVHqAc+OP8BXl30KhsHE2EO+SPTxfyRKMye/BS38jBq1CjRJZBC\nmUv2GnZtiIZdG4ougyrIXPJHpon5I1GYPfnxbEtEVOzmqZvQ3NGg4UtsDoiIiKg0xa08EFFpdxPv\nYt9/9iEuIg7O9Z0xKmEULK0tRZdFRERERobNA5GCZd7IROTnkYhdGouigiIAQPqVdJxadQrt3msn\nuDoiIiIyNoobmN68ebPoEkihjCl7Oek52PPpHsxrNA/HFx0vbhzsa9rj5e9ehucgT8EVktyMKX+k\nPMwficLsyU9xzUNERIToEkihjCV7Wq0WyzssR9SMKBRkFwAArKtYo9PUThhzeQx8x/pCbcNFSXNj\nLPkjZWL+SBRmT34cmCZSoKMLjmL7qO2wtLaE90hvdPy0IxxcHESXRUREREbOaD5eDA0NhVqtRlhY\nGMLCwkSXQ2TW2r3bDmmX09B+THs4uzuLLoeIiIhMBFceiIiIiIioXBQ380BkzrRaLS5uu4g/Rv4B\nwZ8LEBERkRlSXPMwZMgQ0SWQQuk7e1cOXMHKgJVY98o6HF90HJd3X9br/si08L2PRGL+SBRmT35G\nM/NgKMHBwaJLIIXSV/auH7uOvZP24vKfus1CXEQcGnVrpJd9kunhex+JxPyRKMye/DjzQGSibsXd\nwr4p+xC/OV5ne83mNRH0eRCav94cKpVKUHVERERkjhS38kBkLk4sPaHTODg3cEbnqZ3RakArWFgq\n7ohEIiIiMgA2D0QmquOnHXFy2UnYONkgcEogvN7xgqW1peiyiIiIyIwp7uPJqKgo0SWQQsmdvSq1\nq2DAjgEYc2kMXhzxIhsHeiK+95FIzB+JwuzJT3HNw6xZs0SXQApV0ewV5hU+9THuHd1hZWdV2ZJI\nQfjeRyIxfyQKsyc/xQ1MazQa2Nvb630/RI8qb/by7ufh6PdHEfNtDIZEDUGNJjUMUB2ZO773kUjM\nH4nC7MlPcc0DkbEqyCnAiSUnEDUjClk3swAArfq3wutrXxdcGREREZGEA9NEghXmFeLkipOInB6J\nzOuZxdtVFipYWltCW6SFyoKnXCUiIiLx2DwQCXR592X8/u7vSL+SrrO9ed/mCPpvEFxauAiqjIiI\niKg0xQ1MT5gwQXQJpFBlZc+uhp1O49C0V1O8F/se+v3aj40DyYrvfSQS80eiMHvyU9zKg5ubm+gS\nSKHKyp5rW1c0f7058u7nIei/QajrU1dAZaQEfO8jkZg/EoXZkx8HpokEK8gtgNpGcX08ERERmSDF\nHbZEZCharRYXt19ETnrOEx/HxoGIiIhMBZsHIplptVpc3n0ZK/xXYF3PdYieEy26JCIiIiJZKK55\niI+PF10CmbGrkVexuvNqrOm2BteirwEAYubEIPtuNrNHQjF/JBLzR6Iwe/JTXPMQHh4uugQyQ9di\nrmFNtzVY1WkVrkZeLd7u0tIFvVf2hq2zLbNHQjF/JBLzR6Iwe/JT3MB0cnIyJ+9JVlcPXsWqwFU6\n22o0rYFOUzuhZb+WsLCUenRmj0Ri/kgk5o9EYfbkp7jmgUhu2iItfvD6ASmnU+DcwBmdPuuE1gNa\nw0KtuIU9IiIiMnNG0zz06NEDarUaYWFhCAsLE1kSUYVd3n0ZaUlpaDO4DSytLEWXQ0RERKQXRtM8\ncOWBiIiIiMi4Ke64ipkzZ4ougUzInYt3sHnQZpz56cwzPxezRyIxfyQS80eiMHvyU9zVqTQajegS\nyATcTbyLyOmROPPTGWgLtUg+lAyPUI9nmmNg9kgk5o9EYv5IFGZPfjxsieghjzYND9hVt8Og/YNQ\nu1VtgdURERERiaW4lQeismhSNfhzwp84vea0TtNgW80WHf7dAT6jfGBT1UZghURERETisXkgAqC2\nU+PitovFjYNtNVv4jfdD+9Ht2TQQERER/T/FDUynpqaKLoGMkLWDNTqEd4Ctsy2CPg/C2KSxCJwU\nKGvjwOyRSMwficT8kSjMnvwU1zwMHTpUdAlkpF4c+SLGXhmLwMmBsHWylf35mT0SifkjkZg/EoXZ\nk5/iBqZjY2Ph5eWl9/2QcUlLSkNBdgFcWrgIq4HZI5GYPxKJ+SNRmD35Ka55IGVJS0rDwS8O4vTq\n03APdMfbe94WXRIRERGRyeLANJml9CvpiPwiEqdXnUZRQREAIGlvEq5GXoV7oLvg6oiIiIhME5sH\nMivpV9Jx8MuDOLXyVHHTAAA2VW3g+6EvarfmdRqIiIiIKktxA9PLly8XXQLpSe69XCxqtQixS2OL\nGwebqjbo9FknjL0yFp2ndoats/yD0OXF7JFIzB+JxPyRKMye/BTXPMTGxoougfTEpqoNWr/duvh2\n4H8Ci5sGu2p2gqtj9kgs5o9EYv5IFGZPfhyYJrNy79o9nFhyAr7jfGFXXXzDQERERGRO2DyQSdFq\ntVCpVKLLICIiIlIkxR22RKbp9rnb2Nh/I/4Y8YfoUoiIiIgUi2dbIqOWciYFkdMjce7Xc4AWsFBb\nIOCTADi7O4sujYiIiEhxFLfyEBISIroEKocbsTewoc8GLPZcjHO/SI0DANg62yI1PlVscZXE7JFI\nzB+JxPyRKMye/BS38jBq1CjRJdATFOQW4Jc3fsGF/13Q2e5Q2wEdJnSA9/vesHawFlTds2H2SCTm\nj0Ri/kgUZk9+HJgmo7O251okbk8EADg+5wj/j/3h9a4XrOysBFdGREREpGyKW3kg4xc4JRC34m4h\n4JMAtB3SFmpbxpSIiIjIGHDlgYxSUUERLNSKG8khIiIiMmpG89dZaGgoQkJCEBERodf9bN68Wa/P\nT4+n1WqRuCMRZ34689THmmPjwOyRSMwficT8kSjMnvyM5i+09evXY+vWrQgLC9PrfvTdnFBpWq0W\nCb8nYJnPMqztsRY7xu5Abmau6LIMjtkjkZg/Eon5I1GYPfnxsCXSG22RFvFb4hH5eSRunrypc98r\ni1+B93BvQZURERERUWVwEpVkV1RYhLj1cYiaEYXbf93Wua+2Z20ETglE8z7NBVVHRERERJXF5oFk\np1KpSjUOz3k/h8ApgWjaqylUKpXA6oiIiIiostg8kOxUFioEfBKATQM3oZ5/PXSc1BGNuzdm00BE\nRERk4oxmYNpQhgwZIroERfB4ywNDDg7BkIND0KRHEzYOYPZILOaPRGL+SBRmT36Kax6Cg4NFl2Dy\nNKka3Dh544mPsVBbwC3AjU3DQ5g9Eon5I5GYPxKF2ZMfz7ZE5Zb5TyYOzz6ME4tPwMndCSPjRkJl\nweaAiIiISCk480BPlZaUhkMzD+HUylMozCsEAKSeT8X5TefRom8LwdURERERkaGweaDHun3+NqJm\nROHsurPQFpYsUKlt1Wg7rC3q+tQVWB0RERERGZriZh6ioqJEl2ASCvMKsbrzapxZc6a4cbCuYg3/\nj/0x9spY9JzfE071nARXaVqYPRKJ+SORmD8ShdmTn+Kah1mzZokuwSRYWlvCZ4wPAMCuuh06T+uM\nccnj0PWrrqhSu4rg6kwTs0ciMX8kEvNHojB78lPcwLRGo4G9vb3e92MOctJzcHL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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(tif, (r0, 2.001, 6), thickness=2, \n", " legend_label=r'$\\tilde{t}_{\\rm f}$',\n", " axes_labels=[r'$r_0/m$', r'$\\tilde{t}/m$'], gridlines=True)\n", "graph += plot(tih, (r0, 2.001, 6), linestyle='--', thickness=2, \n", " legend_label=r'$\\tilde{t}_{\\rm h}$', color='purple')\n", "graph" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*sqrt(1/2)*pi*sqrt(r0^3)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tauf = pi*sqrt(r0^3/8)\n", "tauf" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sqrt(1/2)*sqrt(r0^3)*(sqrt(2)*sqrt(-(2/r0 - 1)/r0) + arctan(sqrt(1/2*r0 - 1)))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tauh = sqrt(r0^3/2)*(atan(sqrt(r0/2-1)) + sqrt(2/r0*(1-2/r0)))\n", "tauh" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Sh16vt7qO0vOuaB2KYv3r0axZM5vUUZo1dXTv3t1u68qSOornaY91ZUkdpR/f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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(tauf, (r0, 2.001, 6), thickness=2, \n", " legend_label=r'$\\tau_{\\rm f}$',\n", " axes_labels=[r'$r_0/m$', r'$\\tau/m$'], gridlines='minor')\n", "graph += plot(tauh, (r0, 2.001, 6), linestyle='--', thickness=2, \n", " legend_label=r'$\\tau_{\\rm h}$', color='purple')\n", "graph" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"ges_infall_time.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Proper time spent inside the black hole" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/4*(sqrt(2)*pi - 2*sqrt(2)*arctan(sqrt(1/2*r0 - 1)) - 4*sqrt((r0 - 2)/r0^2))*r0^(3/2)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taui = (tauf - tauh).simplify_full()\n", "taui" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "pi" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lim(taui, r0 = 2)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4/3" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lim(taui, r0 = +oo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may check the above limit by asking for a Taylor expansion in terms of $u=1/r_0$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/4*(sqrt(2)*pi - 4*u*sqrt(-(2*u - 1)/u) - 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-(2*u - 1)/u)))/u^(3/2)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('u')\n", "s = taui.subs({r0: 1/u}).simplify_full()\n", "s" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "6/7*u^2 + 4/5*u + 4/3" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.taylor(u, 0, 2)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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aP3++Fi5c6C8gCy12OyRaLHdItESx0mKlQ6LFcodEi+UOyVZLHEz7Kw7Nzc0K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\nMWfOHHw+X0Tf4/P52L59OwUFBRQUFPD111/ToUOHaORJI5W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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(tauf - tauh, (r0, 2.001, 20), thickness=2, \n", " axes_labels=[r'$r_0/m$', r'$\\Delta\\tau_{\\rm in}/m$'], \n", " ymin=1.3, ymax = 3.2, gridlines='minor')\n", "graph" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "graph.save(\"ges_time_inside.pdf\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.1.rc3", "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": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 2 }