SpECTRE Documentation Coverage Report
Current view: top level - PointwiseFunctions/GeneralRelativity - TimeDerivativeOfSpacetimeMetric.hpp Hit Total Coverage
Commit: 9a905b0737f373631c1b8e8389b8f26e67fa5313 Lines: 2 3 66.7 %
Date: 2024-03-28 09:03:18
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          Line data    Source code
       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <cmath>
       7             : #include <cstddef>
       8             : #include <cstdint>
       9             : #include <utility>
      10             : 
      11             : #include "DataStructures/DataBox/Prefixes.hpp"
      12             : #include "DataStructures/DataBox/Tag.hpp"
      13             : #include "DataStructures/Tensor/EagerMath/DeterminantAndInverse.hpp"
      14             : #include "DataStructures/Tensor/Tensor.hpp"
      15             : #include "DataStructures/VariablesTag.hpp"
      16             : #include "NumericalAlgorithms/LinearOperators/PartialDerivatives.hpp"
      17             : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
      18             : #include "Utilities/ContainerHelpers.hpp"
      19             : #include "Utilities/Gsl.hpp"
      20             : #include "Utilities/TMPL.hpp"
      21             : #include "Utilities/TaggedTuple.hpp"
      22             : 
      23             : /// \ingroup GeneralRelativityGroup
      24             : /// Holds functions related to general relativity.
      25             : namespace gr {
      26             : /// @{
      27             : /*!
      28             :  * \ingroup GeneralRelativityGroup
      29             :  * \brief Computes the time derivative of the spacetime metric from spatial
      30             :  * metric, lapse, shift, and their time derivatives.
      31             :  *
      32             :  * \details Computes the derivative as:
      33             :  *
      34             :  * \f{align}{
      35             :  * \partial_t g_{tt} &= - 2 \alpha \partial_t \alpha
      36             :  * - 2 \gamma_{i j} \beta^i \partial_t \beta^j
      37             :  * + \beta^i \beta^j \partial_t \gamma_{i j}\\
      38             :  * \partial_t g_{t i} &= \gamma_{j i} \partial_t \beta^j
      39             :  * + \beta^j \partial_t \gamma_{j i}\\
      40             :  * \partial_t g_{i j} &= \partial_t \gamma_{i j},
      41             :  * \f}
      42             :  *
      43             :  * where \f$\alpha, \beta^i, \gamma_{ij}\f$ are the lapse, shift, and spatial
      44             :  * metric respectively.
      45             :  */
      46             : template <typename DataType, size_t SpatialDim, typename Frame>
      47           1 : void time_derivative_of_spacetime_metric(
      48             :     gsl::not_null<tnsr::aa<DataType, SpatialDim, Frame>*> dt_spacetime_metric,
      49             :     const Scalar<DataType>& lapse, const Scalar<DataType>& dt_lapse,
      50             :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      51             :     const tnsr::I<DataType, SpatialDim, Frame>& dt_shift,
      52             :     const tnsr::ii<DataType, SpatialDim, Frame>& spatial_metric,
      53             :     const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric);
      54             : 
      55             : template <typename DataType, size_t SpatialDim, typename Frame>
      56           1 : tnsr::aa<DataType, SpatialDim, Frame> time_derivative_of_spacetime_metric(
      57             :     const Scalar<DataType>& lapse, const Scalar<DataType>& dt_lapse,
      58             :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      59             :     const tnsr::I<DataType, SpatialDim, Frame>& dt_shift,
      60             :     const tnsr::ii<DataType, SpatialDim, Frame>& spatial_metric,
      61             :     const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric);
      62             : /// @}
      63             : namespace Tags {}  // namespace Tags
      64             : }  // namespace gr

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