Line data    Source code

       1            0 : // Distributed under the MIT License.
       2              : // See LICENSE.txt for details.
       3              : 
       4              : #pragma once
       5              : 
       6              : #include <cstddef>
       7              : 
       8              : #include "DataStructures/Tensor/Tensor.hpp"
       9              : #include "Utilities/Gsl.hpp"
      10              : 
      11              : namespace CurvedScalarWave::Worldtube {
      12              : /*!
      13              :  * \brief The spatial derivative of the zero spin inverse Kerr Schild metric,
      14              :  * $\partial_i g^{\mu \nu}$, assuming a black hole at the coordinate center with
      15              :  * mass M = 1.
      16              :  */
      17            1 : tnsr::iAA<double, 3> spatial_derivative_inverse_ks_metric(
      18              :     const tnsr::I<double, 3>& pos);
      19              : 
      20              : /*!
      21              :  * \brief The spatial derivative of the spacetime metric,
      22              :  * $\partial_i g_{\mu \nu}$.
      23              :  */
      24            1 : tnsr::iaa<double, 3> spatial_derivative_ks_metric(
      25              :     const tnsr::aa<double, 3>& metric,
      26              :     const tnsr::iAA<double, 3>& di_inverse_metric);
      27              : 
      28              : /*!
      29              :  * \brief The second spatial derivative of the zero spin inverse Kerr Schild
      30              :  * metric, $\partial_i \partial_j g^{\mu \nu}$, assuming a black hole at the
      31              :  * coordinate center with mass M = 1.
      32              :  */
      33            1 : tnsr::iiAA<double, 3> second_spatial_derivative_inverse_ks_metric(
      34              :     const tnsr::I<double, 3>& pos);
      35              : 
      36              : /*!
      37              :  * \brief The spatial derivative of the spacetime metric,
      38              :  * $\partial_i \partial_j g_{\mu \nu}$.
      39              :  */
      40            1 : tnsr::iiaa<double, 3> second_spatial_derivative_metric(
      41              :     const tnsr::aa<double, 3>& metric, const tnsr::iaa<double, 3>& di_metric,
      42              :     const tnsr::iAA<double, 3>& di_inverse_metric,
      43              :     const tnsr::iiAA<double, 3>& dij_inverse_metric);
      44              : 
      45              : /*!
      46              :  * \brief The spatial derivative of the Christoffel
      47              :  * symbols, $\partial_i \Gamma^\rho_{\mu \nu}$.
      48              :  */
      49            1 : tnsr::iAbb<double, 3> spatial_derivative_christoffel(
      50              :     const tnsr::iaa<double, 3>& di_metric,
      51              :     const tnsr::iiaa<double, 3>& dij_metric,
      52              :     const tnsr::AA<double, 3>& inverse_metric,
      53              :     const tnsr::iAA<double, 3>& di_inverse_metric);
      54              : 
      55              : /*!
      56              :  * \brief The spatial derivative of the zero spin Kerr Schild contracted
      57              :  * Christoffel symbols,
      58              :  * $\partial_i g^{\mu \nu} \Gamma^\rho_{\mu \nu}$, assuming a black hole at the
      59              :  * coordinate center with mass M = 1.
      60              :  */
      61            1 : tnsr::iA<double, 3> spatial_derivative_ks_contracted_christoffel(
      62              :     const tnsr::I<double, 3>& pos);
      63              : 
      64              : }  // namespace CurvedScalarWave::Worldtube