Line data    Source code

       1            0 : // Distributed under the MIT License.
       2              : // See LICENSE.txt for details.
       3              : 
       4              : #pragma once
       5              : 
       6              : #include "DataStructures/Tensor/Tensor.hpp"
       7              : #include "Utilities/Gsl.hpp"
       8              : 
       9              : namespace ScalarTensor {
      10              : /// @{
      11              : /*!
      12              :  * \brief Normal projection of the second covariant derivative of the scalar
      13              :  * field.
      14              :  *
      15              :  * \details Computes the term
      16              :  * \begin{equation}
      17              :  *   n^a n^b \nabla_a \nabla_b \Psi = - \frac{1}{\alpha} \Bigl[ \partial_t \Pi
      18              :  *      - \beta^i \partial_i \Pi
      19              :  *      + \Phi^i \partial_i \alpha \Bigr],
      20              :  * \end{equation}
      21              :  * where $\Psi$ is the scalar field, $\Pi$ is its conjugate momentum and
      22              :  * $\Phi_i = \partial_i \Psi$; $n^a$ is the unit vector normal to the spatial
      23              :  * hypersurfaces, while $\alpha$ is the lapse and $\beta^i$ is the shift vector.
      24              :  */
      25              : template <typename DataType, typename Frame>
      26            1 : void DDKG_normal_normal_projection(
      27              :     gsl::not_null<Scalar<DataType>*> DDKG_normal_normal_result,
      28              :     const Scalar<DataType>& lapse, const tnsr::I<DataType, 3, Frame>& shift,
      29              :     const tnsr::II<DataType, 3, Frame>& inverse_spatial_metric,
      30              :     const tnsr::i<DataType, 3, Frame>& phi_scalar,
      31              :     const tnsr::i<DataType, 3, Frame>& d_pi_scalar,
      32              :     const Scalar<DataType>& dt_pi_scalar,
      33              :     const tnsr::i<DataType, 3, Frame>& d_lapse);
      34              : 
      35              : template <typename DataType, typename Frame>
      36            1 : Scalar<DataType> DDKG_normal_normal_projection(
      37              :     const Scalar<DataType>& lapse, const tnsr::I<DataType, 3, Frame>& shift,
      38              :     const tnsr::II<DataType, 3, Frame>& inverse_spatial_metric,
      39              :     const tnsr::i<DataType, 3, Frame>& phi_scalar,
      40              :     const tnsr::i<DataType, 3, Frame>& d_pi_scalar,
      41              :     const Scalar<DataType>& dt_pi_scalar,
      42              :     const tnsr::i<DataType, 3, Frame>& d_lapse);
      43              : /// @}
      44              : 
      45              : /// @{
      46              : /*!
      47              :  * \brief Mixed projection of the second covariant derivative of the scalar
      48              :  * field.
      49              :  *
      50              :  * \details Computes the term
      51              :  * \begin{equation}
      52              :  *   \gamma^a_i n^b \nabla_a \nabla_b \Psi
      53              :  *     = - \partial_i \Pi + K_{ij} \Phi^j,
      54              :  * \end{equation}
      55              :  * where $\Psi$ is the scalar field, $\Pi$ is its conjugate momentum and
      56              :  * $\Phi_i = \partial_i \Psi$; $n^a$ is the unit vector normal to the spatial
      57              :  * hypersurfaces, $\gamma^a_b = \delta^a_b + n^a n_b$ is the projection operator
      58              :  * onto them and $K_{ij}$ is the extrinsic curvature.
      59              :  */
      60              : template <typename DataType, typename Frame>
      61            1 : void DDKG_normal_spatial_projection(
      62              :     gsl::not_null<tnsr::i<DataType, 3, Frame>*> DDKG_normal_spatial_result,
      63              :     const tnsr::II<DataType, 3, Frame>& inverse_spatial_metric,
      64              :     const tnsr::ii<DataType, 3, Frame>& extrinsic_curvature,
      65              :     const tnsr::i<DataType, 3, Frame>& phi_scalar,
      66              :     const tnsr::i<DataType, 3, Frame>& d_pi_scalar);
      67              : 
      68              : template <typename DataType, typename Frame>
      69            1 : tnsr::i<DataType, 3, Frame> DDKG_normal_spatial_projection(
      70              :     const tnsr::II<DataType, 3, Frame>& inverse_spatial_metric,
      71              :     const tnsr::ii<DataType, 3, Frame>& extrinsic_curvature,
      72              :     const tnsr::i<DataType, 3, Frame>& phi_scalar,
      73              :     const tnsr::i<DataType, 3, Frame>& d_pi_scalar);
      74              : /// @}
      75              : 
      76              : /// @{
      77              : /*!
      78              :  * \brief Spatial projection of the second covariant derivative of the scalar
      79              :  * field.
      80              :  *
      81              :  * \details Computes the term
      82              :  * \begin{equation}
      83              :  *   \gamma^a_i \gamma^b_j \nabla_a \nabla_b \Psi =
      84              :  *     - \Pi K_{ij} + D_{(i} \Phi_{j)},
      85              :  * \end{equation}
      86              :  * where $\Psi$ is the scalar field, $\Pi$ is its conjugate momentum and
      87              :  * $\Phi_i = \partial_i \Psi$; $n^a$ is the unit vector normal to the spatial
      88              :  * hypersurfaces and $\gamma^a_b = \delta^a_b + n^a n_b$ is the projection
      89              :  * operator onto them; $K_{ij}$ is the extrinsic curvature and $D_i$ is the
      90              :  * covariant derivative with respect to the spatial metric.
      91              :  */
      92              : template <typename DataType, typename Frame>
      93            1 : void DDKG_spatial_spatial_projection(
      94              :     gsl::not_null<tnsr::ii<DataType, 3, Frame>*> DDKG_spatial_spatial_result,
      95              :     const tnsr::ii<DataType, 3, Frame>& extrinsic_curvature,
      96              :     const tnsr::Ijj<DataType, 3, Frame>& spatial_christoffel_second_kind,
      97              :     const Scalar<DataType>& pi_scalar,
      98              :     const tnsr::i<DataType, 3, Frame>& phi_scalar,
      99              :     const tnsr::ij<DataType, 3, Frame>& d_phi_scalar);
     100              : 
     101              : template <typename DataType, typename Frame>
     102            1 : tnsr::ii<DataType, 3, Frame> DDKG_spatial_spatial_projection(
     103              :     const tnsr::ii<DataType, 3, Frame>& extrinsic_curvature,
     104              :     const tnsr::Ijj<DataType, 3, Frame>& spatial_christoffel_second_kind,
     105              :     const Scalar<DataType>& pi_scalar,
     106              :     const tnsr::i<DataType, 3, Frame>& phi_scalar,
     107              :     const tnsr::ij<DataType, 3, Frame>& d_phi_scalar);
     108              : /// @}
     109              : }  // namespace ScalarTensor