gr::Tags::CovariantDerivativeOfExtrinsicCurvatureCompute< SpatialDim, Frame > Struct Template Reference

Computes the spatial covariant derivative of the extrinsic curvature. More...

#include <ExtrinsicCurvature.hpp>

Public Types
using	argument_tags = tmpl::list< ::Tags::deriv< gr::Tags::ExtrinsicCurvature< DataVector, SpatialDim, Frame >, tmpl::size_t< SpatialDim >, Frame >, gr::Tags::ExtrinsicCurvature< DataVector, SpatialDim, Frame >, gr::Tags::SpatialChristoffelSecondKind< DataVector, SpatialDim, Frame > >
using	return_type = tnsr::ijj< DataVector, SpatialDim, Frame >
using	base = gr::Tags::CovariantDerivativeOfExtrinsicCurvature< DataVector, SpatialDim, Frame >
Public Types inherited from gr::Tags::CovariantDerivativeOfExtrinsicCurvature< DataVector, SpatialDim, Frame >
using	type = tnsr::ijj< DataVector, Dim, Frame >

Static Public Attributes
static constexpr auto	function

Detailed Description

template<size_t SpatialDim, typename Frame>
struct gr::Tags::CovariantDerivativeOfExtrinsicCurvatureCompute< SpatialDim, Frame >

Computes the spatial covariant derivative of the extrinsic curvature.

Details

The spatial covariant derivative is computed as

\[ D_k K_{ij} = \partial_k K_{ij} - {^{(3)}\Gamma^{l}_{ki}} K_{lj} - {^{(3)}\Gamma^{l}_{kj}}K_{il} \]

where \( {^{(3)}\Gamma^{k}_{ij}} \) is the spatial Christoffel symbol of the second kind.

Member Data Documentation

function

template<size_t SpatialDim, typename Frame >

constexpr auto gr::Tags::CovariantDerivativeOfExtrinsicCurvatureCompute< SpatialDim, Frame >::function

staticconstexpr

Initial value:

= static_cast<void (*)(
      const gsl::not_null<tnsr::ijj<DataVector, SpatialDim, Frame>*>,
      const tnsr::ijj<DataVector, SpatialDim, Frame>&,
      const tnsr::ii<DataVector, SpatialDim, Frame>&,
      const tnsr::Ijj<DataVector, SpatialDim, Frame>&
          spatial_christoffel_second_kind)>(
      &covariant_derivative_of_extrinsic_curvature<DataVector, SpatialDim,
                                                   Frame>)

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The documentation for this struct was generated from the following file:

• src/PointwiseFunctions/GeneralRelativity/ExtrinsicCurvature.hpp