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              : #include "Utilities/TMPL.hpp"
      11              : 
      12              : /// \ingroup GeneralRelativityGroup
      13              : /// Holds functions related to general relativity.
      14              : namespace gr {
      15              : /// @{
      16              : /*!
      17              :  * \ingroup GeneralRelativityGroup
      18              :  * \brief Computes the time derivative of the spacetime metric from spatial
      19              :  * metric, lapse, shift, and their time derivatives.
      20              :  *
      21              :  * \details Computes the derivative as:
      22              :  *
      23              :  * \f{align}{
      24              :  * \partial_t g_{tt} &= - 2 \alpha \partial_t \alpha
      25              :  * - 2 \gamma_{i j} \beta^i \partial_t \beta^j
      26              :  * + \beta^i \beta^j \partial_t \gamma_{i j}\\
      27              :  * \partial_t g_{t i} &= \gamma_{j i} \partial_t \beta^j
      28              :  * + \beta^j \partial_t \gamma_{j i}\\
      29              :  * \partial_t g_{i j} &= \partial_t \gamma_{i j},
      30              :  * \f}
      31              :  *
      32              :  * where \f$\alpha, \beta^i, \gamma_{ij}\f$ are the lapse, shift, and spatial
      33              :  * metric respectively.
      34              :  */
      35              : template <typename DataType, size_t SpatialDim, typename Frame>
      36            1 : void time_derivative_of_spacetime_metric(
      37              :     gsl::not_null<tnsr::aa<DataType, SpatialDim, Frame>*> dt_spacetime_metric,
      38              :     const Scalar<DataType>& lapse, const Scalar<DataType>& dt_lapse,
      39              :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      40              :     const tnsr::I<DataType, SpatialDim, Frame>& dt_shift,
      41              :     const tnsr::ii<DataType, SpatialDim, Frame>& spatial_metric,
      42              :     const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric);
      43              : 
      44              : template <typename DataType, size_t SpatialDim, typename Frame>
      45            1 : tnsr::aa<DataType, SpatialDim, Frame> time_derivative_of_spacetime_metric(
      46              :     const Scalar<DataType>& lapse, const Scalar<DataType>& dt_lapse,
      47              :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      48              :     const tnsr::I<DataType, SpatialDim, Frame>& dt_shift,
      49              :     const tnsr::ii<DataType, SpatialDim, Frame>& spatial_metric,
      50              :     const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric);
      51              : /// @}
      52              : namespace Tags {}  // namespace Tags
      53              : }  // namespace gr