{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dd11fa39",
   "metadata": {},
   "source": [
    "# Schwarzschild check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "43b4c787",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sp\n",
    "\n",
    "# Import the module\n",
    "import aurel\n",
    "from aurel.solutions import Schwarzschild_isotropic as sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ba13eb78",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " *** N =  32\n",
      "8th order finite difference schemes are defined\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Cosmological constant set to AurelCore.Lambda = 0.00e+00"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gammaup3: $\\gamma^{ij}$ Spatial metric with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Gamma_udd3: ${}^{(3)}{\\Gamma^{k}}_{ij}$ Christoffel symbols of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Ricci_down3: ${}^{(3)}R_{ij}$ Ricci tensor of spatial metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_RicciS: ${}^{(3)}R$ Ricci scalar of spatial metric"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_uddd3: ${}^{(3)}{R^{i}}_{jkl}$ Riemann tensor of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_down3: ${}^{(3)}R_{ijkl}$ Riemann tensor of spatial metric with all spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betax: $\\beta^{x}$ x component of the shift vector with indices up. I assume $\\beta^{x}=0$, if not then please define AurelCore.data['betax'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betay: $\\beta^{y}$ y component of the shift vector with indices up. I assume $\\beta^{y}=0$, if not then please define AurelCore.data['betay'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaz: $\\beta^{z}$ z component of the shift vector with indices up. I assume $\\beta^{z}=0$, if not then please define AurelCore.data['betaz'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaup3: $\\beta^{i}$ Shift vector with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betadown3: $\\beta_{i}$ Shift vector with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Ricci_down3: ${}^{(4)}R_{ij}$ Ricci tensor of spacetime metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Ktrace: $K = \\gamma^{ij}K_{ij}$ Trace of extrinsic curvature"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_down4: ${}^{(4)}R_{\\alpha\\beta\\mu\\nu}$ Riemann tensor of spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_uudd4: ${}^{(4)}{R^{\\alpha\\beta}}_{\\mu\\nu}$ Riemann tensor of spacetime metric with mixed spacetime indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Kretschmann: $K={R^{\\alpha\\beta}}_{\\mu\\nu}{R_{\\alpha\\beta}}^{\\mu\\nu}$ Kretschmann scalar"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated null_ray_exp_out: $\\Theta_{out}$ List of expansion of null rays radially going out"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " *** N =  64\n",
      "8th order finite difference schemes are defined\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Cosmological constant set to AurelCore.Lambda = 0.00e+00"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gammaup3: $\\gamma^{ij}$ Spatial metric with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Gamma_udd3: ${}^{(3)}{\\Gamma^{k}}_{ij}$ Christoffel symbols of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Ricci_down3: ${}^{(3)}R_{ij}$ Ricci tensor of spatial metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_RicciS: ${}^{(3)}R$ Ricci scalar of spatial metric"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_uddd3: ${}^{(3)}{R^{i}}_{jkl}$ Riemann tensor of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_down3: ${}^{(3)}R_{ijkl}$ Riemann tensor of spatial metric with all spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betax: $\\beta^{x}$ x component of the shift vector with indices up. I assume $\\beta^{x}=0$, if not then please define AurelCore.data['betax'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betay: $\\beta^{y}$ y component of the shift vector with indices up. I assume $\\beta^{y}=0$, if not then please define AurelCore.data['betay'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaz: $\\beta^{z}$ z component of the shift vector with indices up. I assume $\\beta^{z}=0$, if not then please define AurelCore.data['betaz'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaup3: $\\beta^{i}$ Shift vector with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betadown3: $\\beta_{i}$ Shift vector with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Ricci_down3: ${}^{(4)}R_{ij}$ Ricci tensor of spacetime metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Ktrace: $K = \\gamma^{ij}K_{ij}$ Trace of extrinsic curvature"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_down4: ${}^{(4)}R_{\\alpha\\beta\\mu\\nu}$ Riemann tensor of spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_uudd4: ${}^{(4)}{R^{\\alpha\\beta}}_{\\mu\\nu}$ Riemann tensor of spacetime metric with mixed spacetime indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Kretschmann: $K={R^{\\alpha\\beta}}_{\\mu\\nu}{R_{\\alpha\\beta}}^{\\mu\\nu}$ Kretschmann scalar"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated null_ray_exp_out: $\\Theta_{out}$ List of expansion of null rays radially going out"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " *** N =  96\n",
      "8th order finite difference schemes are defined\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Cosmological constant set to AurelCore.Lambda = 0.00e+00"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gammaup3: $\\gamma^{ij}$ Spatial metric with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Gamma_udd3: ${}^{(3)}{\\Gamma^{k}}_{ij}$ Christoffel symbols of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Ricci_down3: ${}^{(3)}R_{ij}$ Ricci tensor of spatial metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_RicciS: ${}^{(3)}R$ Ricci scalar of spatial metric"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_uddd3: ${}^{(3)}{R^{i}}_{jkl}$ Riemann tensor of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_down3: ${}^{(3)}R_{ijkl}$ Riemann tensor of spatial metric with all spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betax: $\\beta^{x}$ x component of the shift vector with indices up. I assume $\\beta^{x}=0$, if not then please define AurelCore.data['betax'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betay: $\\beta^{y}$ y component of the shift vector with indices up. I assume $\\beta^{y}=0$, if not then please define AurelCore.data['betay'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaz: $\\beta^{z}$ z component of the shift vector with indices up. I assume $\\beta^{z}=0$, if not then please define AurelCore.data['betaz'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaup3: $\\beta^{i}$ Shift vector with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betadown3: $\\beta_{i}$ Shift vector with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Ricci_down3: ${}^{(4)}R_{ij}$ Ricci tensor of spacetime metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Ktrace: $K = \\gamma^{ij}K_{ij}$ Trace of extrinsic curvature"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_down4: ${}^{(4)}R_{\\alpha\\beta\\mu\\nu}$ Riemann tensor of spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_uudd4: ${}^{(4)}{R^{\\alpha\\beta}}_{\\mu\\nu}$ Riemann tensor of spacetime metric with mixed spacetime indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Kretschmann: $K={R^{\\alpha\\beta}}_{\\mu\\nu}{R_{\\alpha\\beta}}^{\\mu\\nu}$ Kretschmann scalar"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated null_ray_exp_out: $\\Theta_{out}$ List of expansion of null rays radially going out"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " *** N =  128\n",
      "8th order finite difference schemes are defined\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Cosmological constant set to AurelCore.Lambda = 0.00e+00"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gammaup3: $\\gamma^{ij}$ Spatial metric with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Gamma_udd3: ${}^{(3)}{\\Gamma^{k}}_{ij}$ Christoffel symbols of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Ricci_down3: ${}^{(3)}R_{ij}$ Ricci tensor of spatial metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_RicciS: ${}^{(3)}R$ Ricci scalar of spatial metric"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_uddd3: ${}^{(3)}{R^{i}}_{jkl}$ Riemann tensor of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_down3: ${}^{(3)}R_{ijkl}$ Riemann tensor of spatial metric with all spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betax: $\\beta^{x}$ x component of the shift vector with indices up. I assume $\\beta^{x}=0$, if not then please define AurelCore.data['betax'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betay: $\\beta^{y}$ y component of the shift vector with indices up. I assume $\\beta^{y}=0$, if not then please define AurelCore.data['betay'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaz: $\\beta^{z}$ z component of the shift vector with indices up. I assume $\\beta^{z}=0$, if not then please define AurelCore.data['betaz'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaup3: $\\beta^{i}$ Shift vector with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betadown3: $\\beta_{i}$ Shift vector with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Ricci_down3: ${}^{(4)}R_{ij}$ Ricci tensor of spacetime metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Ktrace: $K = \\gamma^{ij}K_{ij}$ Trace of extrinsic curvature"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_down4: ${}^{(4)}R_{\\alpha\\beta\\mu\\nu}$ Riemann tensor of spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_uudd4: ${}^{(4)}{R^{\\alpha\\beta}}_{\\mu\\nu}$ Riemann tensor of spacetime metric with mixed spacetime indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Kretschmann: $K={R^{\\alpha\\beta}}_{\\mu\\nu}{R_{\\alpha\\beta}}^{\\mu\\nu}$ Kretschmann scalar"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated null_ray_exp_out: $\\Theta_{out}$ List of expansion of null rays radially going out"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " *** N =  144\n",
      "8th order finite difference schemes are defined\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Cosmological constant set to AurelCore.Lambda = 0.00e+00"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gammaup3: $\\gamma^{ij}$ Spatial metric with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Gamma_udd3: ${}^{(3)}{\\Gamma^{k}}_{ij}$ Christoffel symbols of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Ricci_down3: ${}^{(3)}R_{ij}$ Ricci tensor of spatial metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_RicciS: ${}^{(3)}R$ Ricci scalar of spatial metric"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_uddd3: ${}^{(3)}{R^{i}}_{jkl}$ Riemann tensor of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_down3: ${}^{(3)}R_{ijkl}$ Riemann tensor of spatial metric with all spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betax: $\\beta^{x}$ x component of the shift vector with indices up. I assume $\\beta^{x}=0$, if not then please define AurelCore.data['betax'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betay: $\\beta^{y}$ y component of the shift vector with indices up. I assume $\\beta^{y}=0$, if not then please define AurelCore.data['betay'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaz: $\\beta^{z}$ z component of the shift vector with indices up. I assume $\\beta^{z}=0$, if not then please define AurelCore.data['betaz'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaup3: $\\beta^{i}$ Shift vector with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betadown3: $\\beta_{i}$ Shift vector with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Ricci_down3: ${}^{(4)}R_{ij}$ Ricci tensor of spacetime metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Ktrace: $K = \\gamma^{ij}K_{ij}$ Trace of extrinsic curvature"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_down4: ${}^{(4)}R_{\\alpha\\beta\\mu\\nu}$ Riemann tensor of spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_uudd4: ${}^{(4)}{R^{\\alpha\\beta}}_{\\mu\\nu}$ Riemann tensor of spacetime metric with mixed spacetime indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Kretschmann: $K={R^{\\alpha\\beta}}_{\\mu\\nu}{R_{\\alpha\\beta}}^{\\mu\\nu}$ Kretschmann scalar"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated null_ray_exp_out: $\\Theta_{out}$ List of expansion of null rays radially going out"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " *** N =  192\n",
      "8th order finite difference schemes are defined\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Cosmological constant set to AurelCore.Lambda = 0.00e+00"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gammaup3: $\\gamma^{ij}$ Spatial metric with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Gamma_udd3: ${}^{(3)}{\\Gamma^{k}}_{ij}$ Christoffel symbols of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Ricci_down3: ${}^{(3)}R_{ij}$ Ricci tensor of spatial metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_RicciS: ${}^{(3)}R$ Ricci scalar of spatial metric"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_uddd3: ${}^{(3)}{R^{i}}_{jkl}$ Riemann tensor of spatial metric with mixed spatial indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated s_Riemann_down3: ${}^{(3)}R_{ijkl}$ Riemann tensor of spatial metric with all spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betax: $\\beta^{x}$ x component of the shift vector with indices up. I assume $\\beta^{x}=0$, if not then please define AurelCore.data['betax'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betay: $\\beta^{y}$ y component of the shift vector with indices up. I assume $\\beta^{y}=0$, if not then please define AurelCore.data['betay'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaz: $\\beta^{z}$ z component of the shift vector with indices up. I assume $\\beta^{z}=0$, if not then please define AurelCore.data['betaz'] = ... "
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betaup3: $\\beta^{i}$ Shift vector with spatial indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated betadown3: $\\beta_{i}$ Shift vector with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Ricci_down3: ${}^{(4)}R_{ij}$ Ricci tensor of spacetime metric with spatial indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Ktrace: $K = \\gamma^{ij}K_{ij}$ Trace of extrinsic curvature"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_down4: ${}^{(4)}R_{\\alpha\\beta\\mu\\nu}$ Riemann tensor of spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Cleaning up cache after 16 calculations..."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: data size before cleanup: 29700.00 MB"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 's_Ricci_down3' used 6 calculations ago (size: 486.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 's_Riemann_uddd3' used 11 calculations ago (size: 4374.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 's_Riemann_down3' used 10 calculations ago (size: 4374.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'gdown4' used 4 calculations ago (size: 864.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'gup4' used 2 calculations ago (size: 864.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removed 5 items"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: data size after cleanup: 18738.00 MB"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gdown4: $g_{\\mu\\nu}$ Spacetime metric with spacetime indices down"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated gup4: $g^{\\mu\\nu}$ Spacetime metric with spacetime indices up"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated st_Riemann_uudd4: ${}^{(4)}{R^{\\alpha\\beta}}_{\\mu\\nu}$ Riemann tensor of spacetime metric with mixed spacetime indices"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Cleaning up cache after 19 calculations..."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: data size before cleanup: 34290.00 MB"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'gammaup3' used 5 calculations ago (size: 486.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'st_Ricci_down3' used 5 calculations ago (size: 486.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'st_Riemann_down4' used 3 calculations ago (size: 13824.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'gdown4' used 2 calculations ago (size: 864.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removed 4 items"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: data size after cleanup: 18630.00 MB"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated Kretschmann: $K={R^{\\alpha\\beta}}_{\\mu\\nu}{R_{\\alpha\\beta}}^{\\mu\\nu}$ Kretschmann scalar"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Cleaning up cache after 20 calculations..."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: data size before cleanup: 18684.00 MB"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removing cached value for 'gup4' used 2 calculations ago (size: 864.00 MB)."
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: Removed 1 items"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "CLEAN-UP: data size after cleanup: 17820.00 MB"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Calculated null_ray_exp_out: $\\Theta_{out}$ List of expansion of null rays radially going out"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 10\n",
    "nt = 0.0\n",
    "NRerror = []\n",
    "NKerror = []\n",
    "NNerror = []\n",
    "allN = [32, 64, 96, 128, 144, 192]\n",
    "for N in allN:\n",
    "    print(\" *** N = \", N)\n",
    "    dx = 2*L / N\n",
    "    param = { 'Nx': N, 'Ny': N, 'Nz': N, \n",
    "            'xmin': -L+0.01, 'ymin': -L+0.01, 'zmin': -L+0.01, \n",
    "            'dx': dx, 'dy': dx, 'dz': dx}\n",
    "    fd = aurel.FiniteDifference(param, fd_order=8)\n",
    "    rel = aurel.AurelCore(fd)\n",
    "    rel.data = sol.data(nt, fd.x, fd.y, fd.z)\n",
    "    rel.freeze_data()\n",
    "    rel.memory_threshold_inGB = 20\n",
    "\n",
    "    R_numerical = rel[\"s_RicciS\"]\n",
    "    Rerror = abs(R_numerical)\n",
    "    NRerror += [np.nanmedian(fd.excision2(Rerror))]\n",
    "\n",
    "    K_numerical = rel[\"Kretschmann\"]\n",
    "    K_exact = sol.Kretschmann(nt, fd.x, fd.y, fd.z)\n",
    "    Kerror = abs((K_numerical - K_exact) / K_exact)\n",
    "    NKerror += [np.nanmedian(fd.excision2(Kerror))]\n",
    "\n",
    "    N_numerical = rel[\"null_ray_exp_out\"]\n",
    "    N_exact = sol.null_ray_exp_out(nt, fd.x, fd.y, fd.z)\n",
    "    Nerror = abs((N_numerical - N_exact) / N_exact)\n",
    "    NNerror += [np.nanmedian(fd.excision2(Nerror))]\n",
    "    \n",
    "    if N != allN[-1]:\n",
    "        del fd, rel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f1f65e86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '8th order FD with excision')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.loglog(allN, NRerror, 'o-', color='C0', label='3 Ricci scalar')\n",
    "order = 8\n",
    "ical = -3\n",
    "converge = [NRerror[ical]*((allN[ical]/allN[i])**(order))for i in range(len(allN))]\n",
    "plt.loglog(allN, converge, '--', color='C0', label='{}th order'.format(order))\n",
    "\n",
    "plt.loglog(allN, NKerror, 'o-', color='C1', label='Kretschmann')\n",
    "order = 8\n",
    "ical = -3\n",
    "converge = [NKerror[ical]*((allN[ical]/allN[i])**(order))for i in range(len(allN))]\n",
    "plt.loglog(allN, converge, '--', color='C1', label='{}th order'.format(order))\n",
    "\n",
    "plt.loglog(allN, NNerror, 'o-', color='C2', label=r'$\\Theta_{out}$')\n",
    "order = 8\n",
    "ical = -3\n",
    "converge = [NNerror[ical]*((allN[ical]/allN[i])**(order))for i in range(len(allN))]\n",
    "plt.loglog(allN, converge, '--', color='C2', label='{}th order'.format(order))\n",
    "\n",
    "plt.grid()\n",
    "plt.xlabel('N')\n",
    "plt.ylabel('Error')\n",
    "plt.legend()\n",
    "plt.title('8th order FD with excision')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d90ee9d1",
   "metadata": {},
   "source": [
    "This shows better than 8th order convergence and a transition from truncation error (from the finite differencing) to floating point noise (from the number of digits stored)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f728277d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}