{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symbolically Understanding Christoffel Symbol and Riemann Curvature Tensor using EinsteinPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "from einsteinpy.symbolic import MetricTensor, ChristoffelSymbols, RiemannCurvatureTensor\n",
    "\n",
    "sympy.init_printing()  # enables the best printing available in an environment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining the metric tensor for 3d spherical coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0\\\\0 & r^{2} & 0\\\\0 & 0 & r^{2} \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0       0     ⎤\n",
       "⎢                 ⎥\n",
       "⎢    2            ⎥\n",
       "⎢0  r       0     ⎥\n",
       "⎢                 ⎥\n",
       "⎢        2    2   ⎥\n",
       "⎣0  0   r ⋅sin (θ)⎦"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "syms = sympy.symbols('r theta phi')\n",
    "# define the metric for 3d spherical coordinates\n",
    "metric = [[0 for i in range(3)] for i in range(3)]\n",
    "metric[0][0] = 1\n",
    "metric[1][1] = syms[0]**2\n",
    "metric[2][2] = (syms[0]**2)*(sympy.sin(syms[1])**2)\n",
    "# creating metric object\n",
    "m_obj = MetricTensor(metric, syms)\n",
    "m_obj.tensor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the christoffel symbols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & 0 & 0\\\\0 & - r & 0\\\\0 & 0 & - r \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & \\frac{1}{r} & 0\\\\\\frac{1}{r} & 0 & 0\\\\0 & 0 & - \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & \\frac{1}{r}\\\\0 & 0 & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}}\\\\\\frac{1}{r} & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                             ⎡             1   ⎤⎤\n",
       "⎢                     ⎡   1                ⎤  ⎢0    0       ─   ⎥⎥\n",
       "⎢⎡0  0       0     ⎤  ⎢0  ─        0       ⎥  ⎢             r   ⎥⎥\n",
       "⎢⎢                 ⎥  ⎢   r                ⎥  ⎢                 ⎥⎥\n",
       "⎢⎢0  -r      0     ⎥  ⎢                    ⎥  ⎢           cos(θ)⎥⎥\n",
       "⎢⎢                 ⎥  ⎢1                   ⎥  ⎢0    0     ──────⎥⎥\n",
       "⎢⎢             2   ⎥  ⎢─  0        0       ⎥  ⎢           sin(θ)⎥⎥\n",
       "⎢⎣0  0   -r⋅sin (θ)⎦  ⎢r                   ⎥  ⎢                 ⎥⎥\n",
       "⎢                     ⎢                    ⎥  ⎢1  cos(θ)        ⎥⎥\n",
       "⎢                     ⎣0  0  -sin(θ)⋅cos(θ)⎦  ⎢─  ──────    0   ⎥⎥\n",
       "⎣                                             ⎣r  sin(θ)        ⎦⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch = ChristoffelSymbols.from_metric(m_obj)\n",
    "ch.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAArCAYAAACuAHIQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVQ4Ee2V0Q2CQAyGD+MA6gi4AToCjmAcgQ30EV51A3UDdQPdwMQNZATjBvj9yJFDiL6qoclv2+tv6d2V4mVZZlxJkiTA34MR9t2NdeWw2ENtwQ2MgQ9qYsnKMFWUP85Ryl6TTm3lzUJLdg/nS07Ds43ENat51CPqDekUXMCZ2AptSrKcT/IlG/z7Mrw4jquz4M3NtDfoHs4v9kY+n7UJXkrN5BkIsCfAx14Aze4r/sbdYMiCgga9RkXoSD6y1I+d/Hr1lUGijD7EYe49x8JGti1jgL0rgiLbjHpKaVe6jkAI8Qj62PZJRQ5j3Jq1qI9Q2kRU8JWszAcFmqQkk021CiqjUUoyURFVwqmRyeID5cdO2vYpfTUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\frac{1}{r}$"
      ],
      "text/plain": [
       "1\n",
       "─\n",
       "r"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ch.tensor()[1,1,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the Riemann Curvature tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]\\\\\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]\\\\\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡⎡0  0  0⎤  ⎡0  0  0⎤  ⎡0  0  0⎤⎤\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎢0  0  0⎥  ⎢0  0  0⎥  ⎢0  0  0⎥⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎣0  0  0⎦  ⎣0  0  0⎦  ⎣0  0  0⎦⎥\n",
       "⎢                               ⎥\n",
       "⎢⎡0  0  0⎤  ⎡0  0  0⎤  ⎡0  0  0⎤⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎢0  0  0⎥  ⎢0  0  0⎥  ⎢0  0  0⎥⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎣0  0  0⎦  ⎣0  0  0⎦  ⎣0  0  0⎦⎥\n",
       "⎢                               ⎥\n",
       "⎢⎡0  0  0⎤  ⎡0  0  0⎤  ⎡0  0  0⎤⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎢0  0  0⎥  ⎢0  0  0⎥  ⎢0  0  0⎥⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎣⎣0  0  0⎦  ⎣0  0  0⎦  ⎣0  0  0⎦⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating Riemann Tensor from Christoffel Symbols\n",
    "rm1 = RiemannCurvatureTensor.from_christoffels(ch)\n",
    "rm1.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]\\\\\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]\\\\\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡⎡0  0  0⎤  ⎡0  0  0⎤  ⎡0  0  0⎤⎤\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎢0  0  0⎥  ⎢0  0  0⎥  ⎢0  0  0⎥⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎣0  0  0⎦  ⎣0  0  0⎦  ⎣0  0  0⎦⎥\n",
       "⎢                               ⎥\n",
       "⎢⎡0  0  0⎤  ⎡0  0  0⎤  ⎡0  0  0⎤⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎢0  0  0⎥  ⎢0  0  0⎥  ⎢0  0  0⎥⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎣0  0  0⎦  ⎣0  0  0⎦  ⎣0  0  0⎦⎥\n",
       "⎢                               ⎥\n",
       "⎢⎡0  0  0⎤  ⎡0  0  0⎤  ⎡0  0  0⎤⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎢⎢0  0  0⎥  ⎢0  0  0⎥  ⎢0  0  0⎥⎥\n",
       "⎢⎢       ⎥  ⎢       ⎥  ⎢       ⎥⎥\n",
       "⎣⎣0  0  0⎦  ⎣0  0  0⎦  ⎣0  0  0⎦⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating Riemann Tensor from Metric Tensor\n",
    "rm2 = RiemannCurvatureTensor.from_metric(m_obj)\n",
    "rm2.tensor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the christoffel symbols for Schwarzschild Spacetime Metric\n",
    "  - The expressions are unsimplified"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAB0CAYAAACR4RnaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAVGUlEQVR4Ae2d27HVRhaGDxTPLsZUOQCcATYRcMhgYCIAMsDFm98onAF2BgMZYCLgkgEOwFXGlBM4839CremtLe2ta6sl/V2l3VJL6su3tFcvLbVa166uri5Shp9//vmmynuh5YMW1m9pean0PxQ7mIAJmIAJjCRwQwr1jvJAyTaF19r/oGnHkLRSqVPWA61/jMp+PiS/qc8p6/NK+f6g9S9T57+l/MSHzpnwl5bvtbxQmjtniEwYzHlCmGVWW2CqNnxSc2430dG+azeiHb9onYPjMPUfFWXwuwr+GBXyRduLKVGVzV3Db1o+a/lRSyMspTuUBMSMzvm54tcklQw/KL6vZeprpix1f5FYmvPEYt8Q02BYxYTua+PfJMSKPYU75LHKpPAQLrXye9gYE0tg5HVb8a998tHxdCrFXYnWn2qdOxiHFgJihAxvKi6UOodpnc6Z7ZdaYvmy22EAAfE05wHcTp2yJaZqy5GeUxrNLxT79VMgptynQrGMCbFFhxJ4w75of3HQgB/yD2UMON2ndCRAJxjfcYXT3mnlcgI5hvz2Hpvz9FfAbpimVOxYxixFkALAMsbKRtE/1Ha1rzjAP7kSQGa4reohyI/9DuMJmPN4hvUcdsP0Rr3lM2/TY/4kJY7vEOXwkxas9rpvX0kOuRHoaI1/m1u911Yfc55eYntjmlSxCy7+9El86tOL3jl2IBCUdrDO41OCFX8zTvT6IALmPAjbyZN2xTSZK+Ykcu/cEgHeS3CYn4A5T894M0w7WezlbcxbcexjjRVj1admr7ow8gJfWT0UPbL2P6nv0DZj5nEDOYwjEKzyplyCRcS4dodxBMx5HL+ms3fFtKti59b7hyZaXdOkWDu94qrjrp3Ks0VxXyidYT4Md2Q8vsMMBMSWYY3k3NTBh7R41NMMtdh+luY8vYz3xrSTYp8Cs8CeVNhTlOE8khDgGcnthpKCxe5nKA1wBiSZ8wBoZ07ZDVP72M9cCd59RIApF3hDtx64o8Plxd2dw3gC5jyeYT2H3TC1Yq+L3tsnCUhx88bbZ8XFG24crHXcMA+1PGLbYTwBcx7PsJ7Dnpgmc8XUIee0LYHTk6OcgiXKvCcftf1OsX32x8LCOn8mNsElc1fb90pmx0c7ZSgBcx5Krv28XTC1YtcFIIXkETPtf4SjPeKFu4WXyxxmJGDO08PdC9Pkil1guYUv5ogpxYbVN8W0rygbFgcTMAET2DWBJXzsjJ7A9cFUuWF4Ii6QO1oGB3UYTAd8NOPZ4Ax9ogmYgAmslEBSxS7Fi3Uehhz9oe3gv36k9Woa2JWydLVNwARMIAsCSV0xUt7FyyuKccVU4521zYNKBxMwARMwgQkIJLXYo/peav1NtO1VEzABEzCBiQgkV+yyznHH8GGNymKfqC3OxgRMwARMQASSumJK4ih2+9M3fvmp4+a9AF5aeqJ1xg47mIAJJCKQXLGXlrqt9UQCXqIYyZgRTrjbCCh4BxMwgYQEkiv2hG1zUQsRkGLnYTjzxlTTDixUFRdrArskkNzHvkvKbrQJmIAJJCSQtcUui+9FyYKPN0zxdmpCtC7KBMYT8H9gPMN6Dntgmq3FLvh88JpJuPj4NS8yMTfJG63z8NXBBDZPwP+B6UW8F6ZZKnbBfyyRMiSyGj2jdeaBYZtP4zmYwKYJ+D8wvXj3xDRLxS6RMtti09uo75R+KQF5pMX0171zzIuA/wPTy2M3THNV7AyV+9wgV6x2QhhK93XLvyawPQL+D0wv090wvTE9u3E5drTGw/c1xxXms2chIBneVsZPtPBHYgZP3GefFIdJ37Tp0EbA/4E2MsPT98Y0O8Uu0QWlHazzWJrBircrJqaS2br+REz25g9xDJeL/wPD2bWduSumubpi2oQT0m+FFccmsFMC/g9ML/jNMM3RYg9WeZPYQq/LuPbVh/L28K0a0ucO5IHOa3qwvHoebkBFYDf/garF86/siml2il1K64sWxNyk7EJaMa/7/NfCvCXQVpUweoIs5XM1b023m7vYXcutdVwXWqhWuN7jKoa0TfwH4obNub43ptkp9lK44StLdVkHi92TiEVk5lJOypcHn6tXICtth/8D0TU+0epumOJj/6aEFuKJGI7Khm+i8h3UesC6ZXIpLF2HGQmI8VNlf2fGIlJmTQdFe9YU/B+YXlpbZ/pdQJblw1P9Cfko9WfF1eyAWucWlPm9H4XKO56HQMn9luLqzd95SkqTq9pR3OGV7UpT6MhSVFf/B0YyrJ++J6a4Yv4pAYS4zmOpbazzZxIGY6IJd7Xc0/bHYss/nQmIGR0kHHnqT/xSaY3uLKXTgcJ9tO9f+WQT1J5ftHzQ8ruWtdzx+T8w/RW0ZaZ/Bly5+tgvyj+fx0IHSY2LfxPPf5GFYhT331raHhoyo+bk8/GoXOb/IVD+99rmBabUgXbRviXK7t1WMaID8n+gN7n2E/bCNEtXTLtYvGcggdj6xmI/ZbE+1MWPG2CyoPxQ6ijzX7Xw9ikutUmD8mXSuMdamBW0MWgf7aJ9dC4OJrBZAlbsmxXt/xsmRRaPbMFiZTKko6DjLpUYH3t0zMAELOTiLkBl8ED2fZ98dM7JO4gyz2JGUOV7TmnTvsk7lj7t8bEmMDcBK/a5CWeUf6kgmd++0b+uqqLw2/aNaQnKNrwgQufBvPrVg/EOGXOX0RqUFyOluBPo0inRvvutmXmHCWyAQLY+9g2wXaQJUnBY5LyZi7sF90Qx8VaZjlLn5ZcXWpp8twwxPWkda/+QQFk8kGXaZQJfw6J+S4RPKpTOxcEENkvAin1DopXiRGk9UczID1weTFdQjAZRzPZTpSsqLNsmxR5b1hw3SVCZDJvMZegkdw6008EENkvAin0jopXyxNL+Q3FwpeCWuEfzlBY/PCWpLXyrHZNa0ir77HQHOqZthE5bPcekw+Wka2dM5j7XBHIgYMWegxSmqcPBy1tSlijoycb8Kz8sftw85wJ3DJWvu6/S1vF0UHXF+6PS39QKfqW0IaN3Ju+8avXypgksTsCKfXERTFYB3AtjFTkKudFNISVK3rM/dFQ5R2PMUepapiqb9uGOcTCBzRLwqJjtiBbFe2DpShl2sbBjAii8gzzinRtZx2Kv7ig20iY3wwQOCGCxc5FjJdmKOUCzug2GKjLqJShmLNPnPVtB58DUDasKZZu5hi+1nPsUH88b6m6dVbXXlTWBFgI8XyvueFHsKAL8miR+0eKwQgJSbqGDHlN7FN4cwx0vVD9eIEKphjdDC5eP0ovhmGMqXba9aZRPU7Yo/753Mk35OM0EciPAtc3/99frudXM9VmOgBRkMaJGMQ9Kpw50PAzH/EH589CT4Y9dXSJdj1OW7UHlFncziifJr70k7zGBZQlYsS/LP8fSsWaL27kpKydlSqfBA9DijgDlqqXT2HYdN1V9sOptrU8pWOeVJQEr9izFslylpESxpvFTF9btxDVh2CJ+/OShbA/tGjJEMnl9XaAJjCFgxT6G3nbP5UHspL52KVR86oWrZyFstId2OZjA5glYsW9exP0bKCXMQ3ReNApzqPfPpHYGeWpZRLGW7aA9HhxQk4s3t0mAUTEOJnBEQEqQB4ybcFuoLZtox5GQaglqZ+cvZdVO9ebGCFixb0ygbs6uCfT5UtauQW298XbFbF3Cbt+eCMSTvfHw266nPUk/aqsVewTDqyawZgKl+yw0gWGdizzTCBVwvBwBu2KWY++STWAWAlLwjABieolFhpbO0ihn2osAFvs35Rkh7pWBDzYBE8iHgJQ5lnqh1Mv1fCrnmsxN4LtQABb7P+VGiMM+xyZgAhkRkKJm1Atv74ZJzPCj85lBPnXIm7zMw8N0EOe+lKVDHDZI4M/QpqxdMZHFwTc8qws4VN7xcgQsm0XYf6tSX5XLc8kg/uwhij1+eLpIBddQ6B6u3Wwfngo+1sc7xdxWMgMg83zwwQWsFIcFCVg26eGX1z1v7nL9o8TDrJiPtN5pzp30tc6vxL1cu1kqdsHnjceb8QWrdYZucQFP+qp7fpde3jWybJaRj7ijzHlpDFdMNTWD0vyAtKNI9nTtZqnYJSeGaTVdsO+UfikB3ewoSx82PQHLZnqmfXK81MHBx97nPB+7I72Sq2Ln4v3ccCWGFy7Y77AMActmGe4XMmhuq2juZCuLfaGqrLXY3Vy72Sn2jtY4D5EcEhOwbBIDPy4OxW5/+jGXsyl7u3ZvnCWS/oCgtIN1HtcgWPF2xcRU0q1bNulYH5VUWuq21o/IdErY1bWbncXeSUQXF7c6HufD0hOwbNIzd4nTENjMtZujxR6s8iZRhV6Xce0O6QlYNj2Zly6Atzqtz13mA533sWdRPvw0gV1du9kpdl3QfJABETX9EUKaP0Z8+iKeZa9l0x8rzHTW6BeHlM9V/9IPz1Ae1w5T9rO1t2s3O8VeXmrhRYz6lRcsdvsZ62TSbVs26VhXJZ1Tytrvj2xUtFpXdnPt3tAFwS1fbj05r003fU0ey+cjvW+r6LxjbgKWzdyEh+Xvj2yc57bpa1d6kS+FFV8Lu66NO1qutDCUKotQVvCzYqyQImgdN8xDLY++pvh3CQKWzRLUO5UZu3v4L9v4qWHb+rWr9j3WUrjscnXFIBIu1GeqaOhw7mr7nrb9UAk6ywbLZln+R6XrfxE/d/JHNo4IVQm7uHazVey6ULE4mPjLITMClk1mAomqI9n4IxsRj/rqXq7dbBV7XSDeNgET+EpAygmLnCG/GD9MMVDM9FimMxsqI8uYo92G0Vdku/td6wtKuxOUG2wCEJCy/qSI6atR5u+1PNNCOtNcP9Xyt9bxs1bPp7TusDMCtth3JnA3d70EpLBxszB9bxjui1/9Hi1SWvzwlCSHHROwYt+x8N301RE4GBUmZY4rxoMJVifG+StsV8z8jF2CCUxF4KYysiKfiuaG87Fi37Bw3bTNEUCph+G/ReNktTe9yLe5hrtB/QjYFdOPl482gSUJ8PUqRr0E5Y4F/3zJCrnsPAlYsecpF9fKBI4ISKHzsPTJ0Y6dJYjDYvPiLFl2HzFbsfeh5WNNwARyILDkvDhLlt2ZvX3snVH5QBMwgUwIxEM7cUsxOihVGFQ2lr6W4EI7W1cdyzsJg4Mt9sHofKIJmMASBKT0JpkXR/k8Vv15ZvF913YMKbssh/cP4noXRSoNZc8bwrx4dqHt8BbxL1p/qWWQ680WOzQdTMAEVkcAxadKo5jDC1t928Cbu+TRO3QtW8fxgPt+Ux3LfaENKPT/lGmhPq+0PWjUkxV7QOjYBExgNQRKhYdS5/sMg5RfeW5hIfdpeM+yqVtb58H88Cjv4Er6rO3LUBel02FdKqZz6BXsiumFywebgAnMTUCKjFEv97W8KcvCXYG7hInNcGkwL84dLU+1rugCF0fjhGfaj686KE7y+EtpuDlQlihWFGfxoSHFlEMa+xhayjbLXe1j+0Jx57I5XoH8j9wpSiNf9tHOEEirh0K5K/F1fcepbSv2U3S8zwRMYAkCfAKzsGYVP5fyQxEHhYpijx9gttZPx2H93uJ8DlKM4iwmR9M6M2CicAvfdrmfvFHgpN3WeqFMFX/QwsPP11o6lV3mR3mhUyEpDnREdRcSx9f98O+UhvK3YhcEBxMwgRUSkOJEuQUrFUUbXCWPtN53OgVcG1j1WOBY/+RbfDpOMYH9bSFWuhxHvfoGzmkrg06H9gU3UpF/QxvpGHqXnbXFHjX6LzWuuhXTusPCBCybNALYG2e1t7BYFWOlVspV2x/7EuecMh+sY+4ACAf5fk06/tV5saUdrx8f3J5Ch9J2Lsr6QWiXYvzwcacTcm3rGML+xvh6Y2oGiWoot17vFPOAhF4b4TAPde/eK4PmbKoKlk0ace6cMxZt8LEPAi5++OHfK2ZUCn50XC/BQh6UZ8+T6KRQ7m0hdrswc2dT3dB38XFteR2kZ6nYJQTGl/JlmMqvpHV6PrbbnjAfNMwb8xCwbObhWs91z5zVdpQZ///KYq/z6bhNPpWyVH5YxEMs4FPKubUqKo+7DOrQFCplrePQabiaqrToBM6vngNE6SdXr5/cu9xOHmA03XrxIIEnyYNAL9ecTZVs2aQR5545o8wqo24kbh6S4md/rAUlX4xQKXXIb+St9cJYLNOKjiBKw8j8UQtjzLmL6Bvwo9OeeqAez7SP8vBEtLW394NTCsrVxw7AJn8TVjuB/W0gigP8MxsBy2Y2tAcZ75azlByW+lhr/aJUlo16QvvQJXSeVWhJQw816aLqvDMroTM5GI6pss62UccUBqziJkv+ZLHZWeyhMSdrfXHBcCiHxAQsmzTAzTkN5xSlSJYocNxKTVb7uSo80wEHnc+5E8L+7BS7KhaUdrDOQ12Jg3+s6MniHV5PQsCySYLZ/4E0mNOUIqWO2+VJxw67qJSOxQWEi6ZJD56teI6K/WyldcCtLgf5mEUIWDZpsJtzGs6TlCIFfeCK6ZDpf3XOYHfUjQ4FpD4kWOVN5QaLkXHtDukJWDZpmK+Os5QQd9FvtfS5m67GcQesyucqrG8xVvs6N6vpWKUV0x+cyyQ7xa6K8xSbejddICGt98OEcyC8/zwBy+Y8oymOWCNn6qy2d37dvo2T8umkuNrOd/pXAtkp9lIw3II0PWwIFvvgWxQLfjQBy2Y0wk4ZmHMnTPMepI5msc/wjWlZroqd13+L8aS1xmER8Jow1oHDMgQsmzTczTkN53OlrOJTePVGZPnwVIq7eEOs7C2LOmsdNwyv3T6qN8Lb6QhYNmlYm3Mazh1Kid1LeBFWYVTmarHDG6C8mRVcMne1fU/bH9npsCgByyYNfnNOw7m1FOmb+HkeXoRB48pbC5hpR7aKXUDpGfsOEZoJk7ONCVg2MY351s15PrZNOYs3ipsRd+geXioKUwZfaJ1pB4ovNinOPmTpismemitoAiawKQJS3Ey0xQtBKPP3WnjrswhKQ+GP+gxfmVWyyIo9GWoXZAImkCOB0hpnsq4w2g73yz3qqjSmD+fzen9rnTH2xReYFGcdYlfMJ1W8Xlk+BbUKn1K94t42ARMwgY4EDgZlSOfhiime5Wk9fnjaMbv5D1O9is/3tZWEYqd3KqaybDgofnDQsNtJJmACJrB6AjfVgrUNymgaDl4J4trV1abf4K0a6hUTMAETaCIg6xd3Cz704Iq50PoLLasdvBG7Ypra7DQTMAET2DoB3M0o9jC0Ggv++Zob/T+maTChTduCYwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{a}{r} + 1 & 0 & 0 & 0\\\\0 & - \\frac{1}{c^{2} \\left(- \\frac{a}{r} + 1\\right)} & 0 & 0\\\\0 & 0 & - \\frac{r^{2}}{c^{2}} & 0\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  a                                      ⎤\n",
       "⎢- ─ + 1       0         0         0      ⎥\n",
       "⎢  r                                      ⎥\n",
       "⎢                                         ⎥\n",
       "⎢             -1                          ⎥\n",
       "⎢   0     ────────────   0         0      ⎥\n",
       "⎢          2 ⎛  a    ⎞                    ⎥\n",
       "⎢         c ⋅⎜- ─ + 1⎟                    ⎥\n",
       "⎢            ⎝  r    ⎠                    ⎥\n",
       "⎢                                         ⎥\n",
       "⎢                         2               ⎥\n",
       "⎢                       -r                ⎥\n",
       "⎢   0          0        ────       0      ⎥\n",
       "⎢                         2               ⎥\n",
       "⎢                        c                ⎥\n",
       "⎢                                         ⎥\n",
       "⎢                               2    2    ⎥\n",
       "⎢                             -r ⋅sin (θ) ⎥\n",
       "⎢   0          0         0    ────────────⎥\n",
       "⎢                                   2     ⎥\n",
       "⎣                                  c      ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "syms = sympy.symbols(\"t r theta phi\")\n",
    "G, M, c, a = sympy.symbols(\"G M c a\")\n",
    "# using metric values of schwarschild space-time\n",
    "# a is schwarzschild radius\n",
    "list2d = [[0 for i in range(4)] for i in range(4)]\n",
    "list2d[0][0] = 1 - (a / syms[1])\n",
    "list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2))\n",
    "list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2)\n",
    "list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2)\n",
    "sch = MetricTensor(list2d, syms)\n",
    "sch.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAABqCAYAAABzo4c6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAOu0lEQVR4Ae1d240ctxKdFfb7Yu0FHMAqg7UdgVcZWPdGYCsDGfqS/gQ5A1kZ2MpAdgSSNgM5gAvoASewPqfV1eL0sqfZnH6wWEWghxw2H1WnWHw3eXJzc7ObYp48eXKJ8H/g+RbuT1Pirh0W9D1r83wP+y6eZ/D7e206ls7PCp9L49hPv3ZcT1KUHyCcAZgXeD7g+Q4PK4Cv4F+s8oO2t6DxKeyXsHewyQP97sFdTQUAXkzwSRmuaSzgegomqcgsQDHzEu/v46GS32cAuB/CYpxiDWj8GcSdwW4Un4TC/an9/xx/79FPuwE/JvhcW0614Ao+3gG7ixh+eHdyJ3jxK9wPeg8VRaNhRXUdIfw1/K7AOHsBNRgrfK4tq1pw5bC3r9Ndg3gaoPocSlFLd/gKfP0W8CZOGabwfQeCvFRoW+FzbdFUgSv0+ZYOwI9Y/sifsOXnf/UmsVX/WjujVvhcW06WcK1O+VFYRLGllQ/LDycsaWro9lvh87PE1vs1g2uNyp9STM5TAlUQxgqfa4uqClxrVH5p3WMFQmr197GXyvys8Lm2WMzgWp3yY8wm3f1Y11781E9sWuFzbc23hGt1yt8Wlj9hX0QKjrT8fF+DscLn2rIygWutys/tx9yJ2DffwuM6qN3777X9t8Ln2nIxgWuVyg/l5vrmB9jNeiZLDtzs8v8Xz0/8X4OxwufasrKC62kqsACEtSEVSFrUt/C7xv/XsLk7sDTDVv4RaJPu//f4/0NLc2m0HkOPFT6PwSgnbvW4njx+/PgSyHBv/10ohvqJsBwpexxHwAoC0HF+D8LdvHt7+63w73w6Ao4AEKhyzO+SdQQcgXEEXPnHMfIQjkCVCLjyVylWZ8oRGEfAlX8cIw/hCFSJgCt/lWJ1phyBcQSS1/nHk9IXAssdsvHnAdxc13XjCJhBwKzyQ9m5v+GqlbR88GNG8M6oI2BZ+bk7kfv8uy3AXhwcAUsI+JjfkrSdV0cgQGBSy49W0sQlGAE+Kpwul2XEVDuuyS0/gOD+f37E8wsefsjzC55XcF8sA72nmoKAyyUFpelhLOCapPwAIno5BCDl8ddaz/afXiIKi+FyWUYgVnBNUn5AXMslBsuUlu1Sdbksg70JXFOVn0tisYMNP7XYy5LZMqLwVIcQcLkMIXOcvwlcT8cwQhcoZQ1czsYbS66Y9+CLcxW8yoiCvsB/Dl/ewS7xYBKQtm9qlcs+l+v/s4TrqPIDflFsaeVDiUhvIKWCCONt7oaQeXAJJy21mirlUoAwzOCa2u0fk8n5WAB/vwkCLpdlYK8C15SWX1r3GIxSSy52CUbbDfsLmU/pXfBace7gq9lsKpeKgTWD66jyQ4l4rz1lHVM+8Vvs7D/mj7yP/ugG6dyQiVyD+Ce5cZeIR1zwMGmRQZiN+C0mlzCzmtyWcB1V/law6i8xGFNevOcef04CsktHm4ccln65h3q5AOcSjQlcU5Wfx3bL1t5QWGyRa7kE4wWU/SsyB5st50c8RbX2pK1nLMilx/Iqf03gmjThB2WwcAlGOLRgy8/hRtHGiFxWl4EVXNny/6dFV+whsKkc1V6CAYGH42P2crjLS4OpWi4bCqBWXL8RTFO7/TsoB1tCzeviwvNBG3xysw8/Xro+GLCQl1bksjbcFnCl8v/TAiv22jivnh8Ey5ady5Os0M7wv9nV1/pT8TmT/gxP9ZXd6uB7hlsj8H8hIGnML4FrsKHQ78AHP0Wmwr/B84h84T8/WX6I5yPcXBb0E34Agpt6EUju9tcAAZSaXfq/YcsSHsf5P5A3+IUTfvRy4whUjYAp5Yck967ohsKz269ibF91KXTmNkHAWrf/zJV9k3LmmRaIgDXlZyvPNfzOoPWPbV7q3rvDEagVAWvdfq7dczZfKgD2BJ7WKlznyxE4hIAp5YfSc4KPB3iYNcBA4zcMZuW1JOOmlH9JIBWlrfEbBkXw6iHV2phfj2SWozRc0uTwhysebgwi4MpvTOjt0Ee41vQNg9Ds9kwIsNsv4+APM6XpyShAAJWAqm8YFECqhURucGvmvdjys+vHgiBHcsHppmYEoPhs8ZuPl1p3zew6b/sIXOEv9X3nE377wKj/B2XmbP49PK9aZli538XDD5W4tZnfMFzieQg3rKbn5x8wEQljZpLyo7DIhhh+EdcVqFIx00bvTDiyB8eTaPg8BQa/4hGFp/KHE34zZVlnMrWXn+QJv7YAqbmoUxu9c6gPeGYrL+fPUdHlApKf4Oa9im4SEbBQfpKUH0CouqhTG72J5XE0GPimwnMCl91++XJxBz//eGkUvS8BgJeq8v6F8mmuJOVHktouLtRG7zSpjYfmpI6M+cdDe4g+AibKT6ryszDFlgJlgwjfl2S00Tsbdmi12PXn6URdyz9b4nYSMlF+RpUfhYgfv4yZYpYJtdE7BmzGeyq/j+8zgGMUS+XnNAEjUWxp5cMo0htIqSDCeEu6tdE7KxYovGzxvdXPR9VM+Rlt+RMxPE8MV0owbfSWgpvT8RmBKspPSssvrXtM8FJLct2/FKONXulqHn0ZKVr9o+4jpACRRum3FC1dztSVn1xARpUfhUHVhZDa6G0VjkOqozffuOLmqsGXeBrLzxfqp7lGlb9NjmNITiT1jbT8pY0xtdHbx3WR/yjYfpBHGrImyk+q8mu7uFAbvWlF8vhQfpBHGoYmyk/ShB9aDFUXdWqjN608zhIqHFqwJxdbwZklI82JWCk/qS0/ZcmCo+miTm30Lq4vKNTc+ivGD/IQJOJ29eUnWflRcNhKqPn0Uxu98fKX7wv+qdxchaHcuvsImSLe+UEeBOKAsVB+krr9BzDyVwUigIIbvY+QpOKdH+RRoMy2IMmVfwvUF8wTys1WnV/3yQoMu/pyHyG/6/fLSBfEX1PSyd1+TUwZp3XwPkJUCOGEn3GYnH1v+esrA2dg6bo+tpyjuRFw5Z8b0e3To+JfhGS04/zQy92OwM67/fUVAr+PsD6ZLsKRK/8isG6XKFp5uYdhOyIKyBk4bLqVeev8U0Tgyp+CkofRiMDWW5m3zn9UZj7mH4XIAyhFIFzZ4BzI2luZs/JnjwHP3pzNEP4Ix2XbbOMtfzZ0HrFkBKAYs2xlRjo8yZe3G/GeimSTk3+bl5zA3OUFf1YG3F3LzVs7/G+OZKeN5zmerGvnveUnmm6qRYDKAeaovLLpaSqvbxChud5qakSGT80f4bhEe69PZ+svPFDp/9f6MXmaP/BfLtP57JP468qfCJQH04dAqxRH3UmINK7xyOUnk0CYmD8VOFbJ8PNiKrgMW3jS0JUQAn9WalewWXlMMt7tnwSXBy4FART22e4kRFocO4tysXv/Hn7sUlOhqHxUruZ4M9gXrR/fcVmV//l8j3f83xi45Yq01DsRmcde973Ni/68hEUM8+qbpgKA56RTm135+zD6fy0I8BSpplWEnX0nIRSLreg5bBlHU7lYsezgxyPsqJDNWLv145icSk6/C7gbhYP9Fg8n6+R/OOHHqIMGcZinVD5hOI7z+8MVhg3nMxj+NR5WEK78RMNNvQi0yiKtHZVRuuW8k3Dq1mZ2o9k6syXnLUdMl4fXiOH7IRMqJsPFWuWhuKE/48XyYcVE/mRM36Qf4ZEVx+S874QUuNsR0IAACr/MiB99J2GrSEyHysOexEc83+EZNYgbttahezRuLwArnlh80sQ5i+aBmxVEWDHhb2NiFYe8G7QndftBhNRAPCTCr+gehHXdF9rkMiM6bBm7cXZOusDuEvHewG7G1bC5tMdyntxtz8m3F4fdeFYAMRN28fnFZowuVhJhuFg6t/ySW36AwgkMv6L7FoTbemiTy1xogW8W+DnuJGQ60qjtkG5zXmUGnUPKO5oU8rxGINLRN51CIwxXAjis6fyCwIzbzUsE/geddw6+bV8iQ1VXFmujN0UGsTBW+IzxDj8W+EkTXAPp0JsTexz3/4yHFUEz6w43FfoFA8DdLMO1fk1lEfhRPzhU4Bo8eyM5hkOZfgVAOnhuJvN7BXuI38mTfSQwtdvPrhVrp77hLGMzWQLCYmOWfvi1/mujNxcXK3zewgfljZNt4YTbrTApHq1CRZWqLdN7w4oBP/YWYmPxFBIkjFQ63TmZKTwiTNPjgB3rEUjaUTup5UdM1maxSQVR+NzaLkrUDJ7a6M1l2QqfufioidcqOocx/dZ/jIdHCLBXQY1FkPejyi81i0QYsOXmnoHX63lrozcXGSt85uKjMR5kym7+g0TZ7hCOww0OB6QRnsT2qPIjNVHsWAbSG2i6HpNyXi6wNnpzkbDCZy4+KuNBkbtufwIDvyN89tAnRfkTaNidpwQqKIw2enOhs8JnLj5FxkttyVPDDTF5OvQi8JfWPfDqnNL6cN2/FKON3lzcVPKJAste4l94pvQW7yPetQAF99FXkUtaNdrAJ+ma9VHlR0JcBiFGMWGJ3+SZxqVA10ZvLg5a+STd4Dm2USUZCqSRVLiTEzQacFT5W1w4rojNQkrLnz3uWAh3bfTmwmCFz1x8VomHyogfAlE/OMyizQM2StMJkLVvUpWfe56bjQ370ZsanN87szYvyWijNxc7K3zm4rNWvOLP64sBkTThB+Vutjy2NVyTDtzs8u/dDhPLYAs/bfTmYmSFz1x8VowXDmPY8pfWGEahSG35GZkM+hXdURg39dQml03BWiJzVMLhnBd7yFmbbpag7VCaycoPBlmbTVmDPJTv4u+00ZsLiBU+c/GZOx7wpnJzdYv6wB15cpbADm7u/2+ODYNdvAmV/x2I7xP8En4qarE+4f7fEZgbAegCv5zjDrw/8VzCzSVLOQGIlQIVn6tjz/Bs3lCCBtLLYUjUUPnZZWm+YoqECLszkdfu5QjYQACKxFadX97JLD51I7z6nJVB6nl9a4EWm6Tv8j65ufH9Eh0a7nAEBhCA0vOEH35PH/0CcCBa0d5Js/1Fc+DEOQLrIMDVrW6X4TpZLpuLK/+y+Hrq9SBAxd8bP6MXcLBbXTrr4YRf6bQ6fY7Alghw4psTelIBsCfwdEuCjs37X8yL21WZi73EAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & - \\frac{1}{c^{2}} & 0 & 0\\\\0 & 0 & - \\frac{r^{2}}{c^{2}} & 0\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1   0    0         0      ⎤\n",
       "⎢                          ⎥\n",
       "⎢   -1                     ⎥\n",
       "⎢0  ───   0         0      ⎥\n",
       "⎢     2                    ⎥\n",
       "⎢    c                     ⎥\n",
       "⎢                          ⎥\n",
       "⎢          2               ⎥\n",
       "⎢        -r                ⎥\n",
       "⎢0   0   ────       0      ⎥\n",
       "⎢          2               ⎥\n",
       "⎢         c                ⎥\n",
       "⎢                          ⎥\n",
       "⎢                2    2    ⎥\n",
       "⎢              -r ⋅sin (θ) ⎥\n",
       "⎢0   0    0    ────────────⎥\n",
       "⎢                    2     ⎥\n",
       "⎣                   c      ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# single substitution\n",
    "subs1 = sch.subs(a,0)\n",
    "subs1.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & -1 & 0 & 0\\\\0 & 0 & - r^{2} & 0\\\\0 & 0 & 0 & - r^{2} \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0    0        0     ⎤\n",
       "⎢                       ⎥\n",
       "⎢0  -1   0        0     ⎥\n",
       "⎢                       ⎥\n",
       "⎢         2             ⎥\n",
       "⎢0  0   -r        0     ⎥\n",
       "⎢                       ⎥\n",
       "⎢              2    2   ⎥\n",
       "⎣0  0    0   -r ⋅sin (θ)⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# multiple substitution\n",
    "subs2 = sch.subs([(a,0), (c,1)])\n",
    "subs2.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{a}{2 r^{2} \\left(- \\frac{a}{r} + 1\\right)} & 0 & 0\\\\\\frac{a}{2 r^{2} \\left(- \\frac{a}{r} + 1\\right)} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}\\frac{a c^{2} \\left(- \\frac{a}{r} + 1\\right)}{2 r^{2}} & 0 & 0 & 0\\\\0 & - \\frac{a}{2 r^{2} \\left(- \\frac{a}{r} + 1\\right)} & 0 & 0\\\\0 & 0 & - r \\left(- \\frac{a}{r} + 1\\right) & 0\\\\0 & 0 & 0 & - r \\left(- \\frac{a}{r} + 1\\right) \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{r} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{r}\\\\0 & 0 & 0 & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}}\\\\0 & \\frac{1}{r} & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                        ⎡   2 ⎛  a    ⎞                      \n",
       "⎢                                        ⎢a⋅c ⋅⎜- ─ + 1⎟                      \n",
       "⎢                                        ⎢     ⎝  r    ⎠                      \n",
       "⎢⎡                      a             ⎤  ⎢──────────────        0             \n",
       "⎢⎢      0         ──────────────  0  0⎥  ⎢        2                           \n",
       "⎢⎢                   2 ⎛  a    ⎞      ⎥  ⎢     2⋅r                            \n",
       "⎢⎢                2⋅r ⋅⎜- ─ + 1⎟      ⎥  ⎢                                    \n",
       "⎢⎢                     ⎝  r    ⎠      ⎥  ⎢                     -a             \n",
       "⎢⎢                                    ⎥  ⎢      0         ──────────────      \n",
       "⎢⎢      a                             ⎥  ⎢                   2 ⎛  a    ⎞      \n",
       "⎢⎢──────────────        0         0  0⎥  ⎢                2⋅r ⋅⎜- ─ + 1⎟      \n",
       "⎢⎢   2 ⎛  a    ⎞                      ⎥  ⎢                     ⎝  r    ⎠      \n",
       "⎢⎢2⋅r ⋅⎜- ─ + 1⎟                      ⎥  ⎢                                    \n",
       "⎢⎢     ⎝  r    ⎠                      ⎥  ⎢                                   ⎛\n",
       "⎢⎢                                    ⎥  ⎢      0               0         -r⋅⎜\n",
       "⎢⎢      0               0         0  0⎥  ⎢                                   ⎝\n",
       "⎢⎢                                    ⎥  ⎢                                    \n",
       "⎢⎣      0               0         0  0⎦  ⎢                                    \n",
       "⎢                                        ⎢      0               0             \n",
       "⎣                                        ⎣                                    \n",
       "\n",
       "                              ⎤                                               \n",
       "                              ⎥                                               \n",
       "                              ⎥                                               \n",
       " 0                 0          ⎥                                               \n",
       "                              ⎥                             ⎡0  0    0       0\n",
       "                              ⎥  ⎡0  0  0        0       ⎤  ⎢                 \n",
       "                              ⎥  ⎢                       ⎥  ⎢                1\n",
       "                              ⎥  ⎢      1                ⎥  ⎢0  0    0       ─\n",
       " 0                 0          ⎥  ⎢0  0  ─        0       ⎥  ⎢                r\n",
       "                              ⎥  ⎢      r                ⎥  ⎢                 \n",
       "                              ⎥  ⎢                       ⎥  ⎢              cos\n",
       "                              ⎥  ⎢   1                   ⎥  ⎢0  0    0     ───\n",
       "                              ⎥  ⎢0  ─  0        0       ⎥  ⎢              sin\n",
       "  a    ⎞                      ⎥  ⎢   r                   ⎥  ⎢                 \n",
       "- ─ + 1⎟           0          ⎥  ⎢                       ⎥  ⎢   1  cos(θ)     \n",
       "  r    ⎠                      ⎥  ⎣0  0  0  -sin(θ)⋅cos(θ)⎦  ⎢0  ─  ──────    0\n",
       "                              ⎥                             ⎣   r  sin(θ)     \n",
       "             ⎛  a    ⎞    2   ⎥                                               \n",
       " 0        -r⋅⎜- ─ + 1⎟⋅sin (θ)⎥                                               \n",
       "             ⎝  r    ⎠        ⎦                                               \n",
       "\n",
       "    ⎤\n",
       "    ⎥\n",
       "    ⎥\n",
       "    ⎥\n",
       "   ⎤⎥\n",
       "   ⎥⎥\n",
       "   ⎥⎥\n",
       "   ⎥⎥\n",
       "   ⎥⎥\n",
       "   ⎥⎥\n",
       "(θ)⎥⎥\n",
       "───⎥⎥\n",
       "(θ)⎥⎥\n",
       "   ⎥⎥\n",
       "   ⎥⎥\n",
       "   ⎥⎥\n",
       "   ⎦⎥\n",
       "    ⎥\n",
       "    ⎥\n",
       "    ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch_ch = ChristoffelSymbols.from_metric(sch)\n",
    "sch_ch.tensor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the simplified expressions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{a}{2 r \\left(- a + r\\right)} & 0 & 0\\\\\\frac{a}{2 r \\left(- a + r\\right)} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}\\frac{a c^{2} \\left(- a + r\\right)}{2 r^{3}} & 0 & 0 & 0\\\\0 & \\frac{a}{2 r \\left(a - r\\right)} & 0 & 0\\\\0 & 0 & a - r & 0\\\\0 & 0 & 0 & \\left(a - r\\right) \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{r} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\frac{\\sin{\\left(2 \\theta \\right)}}{2}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{r}\\\\0 & 0 & 0 & \\frac{1}{\\tan{\\left(\\theta \\right)}}\\\\0 & \\frac{1}{r} & \\frac{1}{\\tan{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                    ⎡   2                                    \n",
       "⎢                                    ⎢a⋅c ⋅(-a + r)                           \n",
       "⎢⎡                   a            ⎤  ⎢─────────────       0         0         \n",
       "⎢⎢     0        ────────────  0  0⎥  ⎢        3                               \n",
       "⎢⎢              2⋅r⋅(-a + r)      ⎥  ⎢     2⋅r                                \n",
       "⎢⎢                                ⎥  ⎢                                        \n",
       "⎢⎢     a                          ⎥  ⎢                    a                   \n",
       "⎢⎢────────────       0        0  0⎥  ⎢      0        ───────────    0         \n",
       "⎢⎢2⋅r⋅(-a + r)                    ⎥  ⎢               2⋅r⋅(a - r)              \n",
       "⎢⎢                                ⎥  ⎢                                        \n",
       "⎢⎢     0             0        0  0⎥  ⎢      0             0       a - r       \n",
       "⎢⎢                                ⎥  ⎢                                        \n",
       "⎢⎣     0             0        0  0⎦  ⎢                                        \n",
       "⎣                                    ⎣      0             0         0    (a - \n",
       "\n",
       "          ⎤                                               ⎤\n",
       "          ⎥  ⎡0  0  0      0     ⎤  ⎡0  0    0       0   ⎤⎥\n",
       "  0       ⎥  ⎢                   ⎥  ⎢                    ⎥⎥\n",
       "          ⎥  ⎢      1            ⎥  ⎢                1   ⎥⎥\n",
       "          ⎥  ⎢0  0  ─      0     ⎥  ⎢0  0    0       ─   ⎥⎥\n",
       "          ⎥  ⎢      r            ⎥  ⎢                r   ⎥⎥\n",
       "          ⎥  ⎢                   ⎥  ⎢                    ⎥⎥\n",
       "  0       ⎥  ⎢   1               ⎥  ⎢                1   ⎥⎥\n",
       "          ⎥  ⎢0  ─  0      0     ⎥  ⎢0  0    0     ──────⎥⎥\n",
       "          ⎥  ⎢   r               ⎥  ⎢              tan(θ)⎥⎥\n",
       "  0       ⎥  ⎢                   ⎥  ⎢                    ⎥⎥\n",
       "          ⎥  ⎢         -sin(2⋅θ) ⎥  ⎢   1    1           ⎥⎥\n",
       "      2   ⎥  ⎢0  0  0  ──────────⎥  ⎢0  ─  ──────    0   ⎥⎥\n",
       "r)⋅sin (θ)⎦  ⎣             2     ⎦  ⎣   r  tan(θ)        ⎦⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplified = sch_ch.simplify()\n",
    "simplified"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}