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/TypeAliases.hpp"
       9              : #include "Utilities/Gsl.hpp"
      10              : 
      11              : namespace gh {
      12              : /// @{
      13              : /*!
      14              :  * \ingroup GeneralRelativityGroup
      15              :  * \brief Computes time derivative of index lowered shift from generalized
      16              :  *        harmonic variables, spatial metric and its time derivative.
      17              :  *
      18              :  * \details The time derivative of \f$ \beta_i \f$ is given by:
      19              :  * \f{align*}
      20              :  *  \partial_0 \beta_i =
      21              :  *      \gamma_{ij} \partial_0 \beta^j + \beta^j \partial_0 \gamma_{ij}
      22              :  * \f}
      23              :  * where the first term is obtained from `time_deriv_of_shift()`, and the latter
      24              :  * is a user input.
      25              :  */
      26              : template <typename DataType, size_t SpatialDim, typename Frame>
      27            1 : void time_deriv_of_lower_shift(
      28              :     gsl::not_null<tnsr::i<DataType, SpatialDim, Frame>*> dt_lower_shift,
      29              :     const Scalar<DataType>& lapse,
      30              :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      31              :     const tnsr::ii<DataType, SpatialDim, Frame>& spatial_metric,
      32              :     const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
      33              :     const tnsr::iaa<DataType, SpatialDim, Frame>& phi,
      34              :     const tnsr::aa<DataType, SpatialDim, Frame>& pi);
      35              : 
      36              : template <typename DataType, size_t SpatialDim, typename Frame>
      37            1 : tnsr::i<DataType, SpatialDim, Frame> time_deriv_of_lower_shift(
      38              :     const Scalar<DataType>& lapse,
      39              :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      40              :     const tnsr::ii<DataType, SpatialDim, Frame>& spatial_metric,
      41              :     const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
      42              :     const tnsr::iaa<DataType, SpatialDim, Frame>& phi,
      43              :     const tnsr::aa<DataType, SpatialDim, Frame>& pi);
      44              : /// @}
      45              : }  // namespace gh