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