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