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