TimeDerivativeOfSpacetimeMetric.hpp
2 // See LICENSE.txt for details.
3
4 #pragma once
5
6 #include <cstddef>
7
9 #include "DataStructures/DataBox/Tag.hpp"
10 #include "DataStructures/DataVector.hpp"
12 #include "Evolution/Systems/GeneralizedHarmonic/Tags.hpp"
14 #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
15 #include "Utilities/ContainerHelpers.hpp"
16 #include "Utilities/Gsl.hpp"
17 #include "Utilities/TMPL.hpp"
18
19 // IWYU pragma: no_forward_declare Tags::deriv
20
21 /// \cond
22 namespace domain {
23 namespace Tags {
24 template <size_t Dim, typename Frame>
25 struct Coordinates;
26 } // namespace Tags
27 } // namespace domain
28 class DataVector;
29 template <typename X, typename Symm, typename IndexList>
30 class Tensor;
31 /// \endcond
32
33 namespace GeneralizedHarmonic {
34 // @{
35 /*!
36  * \ingroup GeneralRelativityGroup
37  * \brief Computes the time derivative of the spacetime metric from the
38  * generalized harmonic quantities \f$\Pi_{a b}\f$, \f$\Phi_{i a b}\f$, and the
39  * lapse \f$\alpha\f$ and shift \f$\beta^i\f$.
40  *
41  * \details Computes the derivative as:
42  *
43  * \f{align}{
44  * \partial_t \psi_{a b} = \beta^i \Phi_{i a b} - \alpha \Pi_{a b}.
45  * \f}
46  */
47 template <size_t SpatialDim, typename Frame, typename DataType>
49  gsl::not_null<tnsr::aa<DataType, SpatialDim, Frame>*> dt_spacetime_metric,
50  const Scalar<DataType>& lapse,
51  const tnsr::I<DataType, SpatialDim, Frame>& shift,
52  const tnsr::aa<DataType, SpatialDim, Frame>& pi,
53  const tnsr::iaa<DataType, SpatialDim, Frame>& phi) noexcept;
54
55 template <size_t SpatialDim, typename Frame, typename DataType>
56 tnsr::aa<DataType, SpatialDim, Frame> time_derivative_of_spacetime_metric(
57  const Scalar<DataType>& lapse,
58  const tnsr::I<DataType, SpatialDim, Frame>& shift,
59  const tnsr::aa<DataType, SpatialDim, Frame>& pi,
60  const tnsr::iaa<DataType, SpatialDim, Frame>& phi) noexcept;
61 //@}
62 } // namespace GeneralizedHarmonic
GeneralizedHarmonic::pi
void pi(gsl::not_null< tnsr::aa< DataType, SpatialDim, Frame > * > pi, const Scalar< DataType > &lapse, const Scalar< DataType > &dt_lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::I< DataType, SpatialDim, Frame > &dt_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ii< DataType, SpatialDim, Frame > &dt_spatial_metric, const tnsr::iaa< DataType, SpatialDim, Frame > &phi) noexcept
Computes the conjugate momentum of the spacetime metric .
GeneralizedHarmonic
Items related to evolving the first-order generalized harmonic system.
Definition: Characteristics.cpp:21
gr::lapse
Scalar< DataType > lapse(const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric) noexcept
Compute lapse from shift and spacetime metric.
cstddef
DataVector
Stores a collection of function values.
Definition: DataVector.hpp:42
GeneralizedHarmonic::phi
void phi(gsl::not_null< tnsr::iaa< DataType, SpatialDim, Frame > * > phi, const Scalar< DataType > &lapse, const tnsr::i< DataType, SpatialDim, Frame > &deriv_lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::iJ< DataType, SpatialDim, Frame > &deriv_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ijj< DataType, SpatialDim, Frame > &deriv_spatial_metric) noexcept
Computes the auxiliary variable used by the generalized harmonic formulation of Einstein's equations...
GeneralizedHarmonic::time_derivative_of_spacetime_metric
void time_derivative_of_spacetime_metric(gsl::not_null< tnsr::aa< DataType, SpatialDim, Frame > * > dt_spacetime_metric, const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::aa< DataType, SpatialDim, Frame > &pi, const tnsr::iaa< DataType, SpatialDim, Frame > &phi) noexcept
Computes the time derivative of the spacetime metric from the generalized harmonic quantities ,...
gr::shift
tnsr::I< DataType, SpatialDim, Frame > shift(const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric, const tnsr::II< DataType, SpatialDim, Frame > &inverse_spatial_metric) noexcept
Compute shift from spacetime metric and inverse spatial metric.
Scalar
Tensor< T, Symmetry<>, index_list<> > Scalar
Definition: TypeAliases.hpp:21
Gsl.hpp
Tensor.hpp
PartialDerivatives.hpp
Prefixes.hpp
TMPL.hpp
gsl::not_null
Require a pointer to not be a nullptr
Definition: Gsl.hpp:183