gr Namespace Reference

Holds functions related to general relativity. More...

Namespaces
	Solutions
	Classes which implement analytic solutions to Einstein's equations.

Classes
class	KerrSchildCoords
	Contains helper functions for transforming tensors in Kerr spacetime to Kerr-Schild coordinates. More...

Typedefs
template<size_t Dim, typename DataType >
using	analytic_solution_tags = tmpl::list< gr::Tags::Lapse< DataType >, ::Tags::dt< gr::Tags::Lapse< DataType > >, ::Tags::deriv< gr::Tags::Lapse< DataType >, tmpl::size_t< Dim >, Frame::Inertial >, gr::Tags::Shift< Dim, Frame::Inertial, DataType >, ::Tags::dt< gr::Tags::Shift< Dim, Frame::Inertial, DataType > >, ::Tags::deriv< gr::Tags::Shift< Dim, Frame::Inertial, DataType >, tmpl::size_t< Dim >, Frame::Inertial >, gr::Tags::SpatialMetric< Dim, Frame::Inertial, DataType >, ::Tags::dt< gr::Tags::SpatialMetric< Dim, Frame::Inertial, DataType > >, ::Tags::deriv< gr::Tags::SpatialMetric< Dim, Frame::Inertial, DataType >, tmpl::size_t< Dim >, Frame::Inertial >, gr::Tags::SqrtDetSpatialMetric< DataType >, gr::Tags::ExtrinsicCurvature< Dim, Frame::Inertial, DataType >, gr::Tags::InverseSpatialMetric< Dim, Frame::Inertial, DataType > >
	The tags for the variables returned by GR analytic solutions.

Functions
template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType >
void	christoffel_first_kind (const gsl::not_null< tnsr::abb< DataType, SpatialDim, Frame, Index > *> christoffel, const tnsr::abb< DataType, SpatialDim, Frame, Index > &d_metric) noexcept
template<size_t Dim, typename Frame , typename DataType >
void	spacetime_metric (const gsl::not_null< tnsr::aa< DataType, Dim, Frame > *> spacetime_metric, const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric) noexcept
template<size_t Dim, typename Frame , typename DataType >
tnsr::aa< DataType, Dim, Frame >	spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric) noexcept
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::ii< DataType, SpatialDim, Frame >	spatial_metric (const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric) noexcept
	Compute spatial metric from spacetime metric. More...
template<size_t Dim, typename Frame , typename DataType >
tnsr::AA< DataType, Dim, Frame >	inverse_spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::II< DataType, Dim, Frame > &inverse_spatial_metric) noexcept
template<size_t SpatialDim, typename Frame , typename DataType >
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. More...
template<size_t SpatialDim, typename Frame , typename DataType >
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. More...
template<size_t Dim, typename Frame , typename DataType >
tnsr::abb< DataType, Dim, Frame >	derivatives_of_spacetime_metric (const Scalar< DataType > &lapse, const Scalar< DataType > &dt_lapse, const tnsr::i< DataType, Dim, Frame > &deriv_lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::I< DataType, Dim, Frame > &dt_shift, const tnsr::iJ< DataType, Dim, Frame > &deriv_shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric, const tnsr::ii< DataType, Dim, Frame > &dt_spatial_metric, const tnsr::ijj< DataType, Dim, Frame > &deriv_spatial_metric) noexcept
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::a< DataType, SpatialDim, Frame >	spacetime_normal_one_form (const Scalar< DataType > &lapse) noexcept
	Computes spacetime normal one-form from lapse. More...
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::A< DataType, SpatialDim, Frame >	spacetime_normal_vector (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift) noexcept
	Computes spacetime normal vector from lapse and shift. More...
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::ii< DataType, SpatialDim, Frame >	extrinsic_curvature (const Scalar< DataType > &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::ii< DataType, SpatialDim, Frame > &dt_spatial_metric, const tnsr::ijj< DataType, SpatialDim, Frame > &deriv_spatial_metric) noexcept
	Computes extrinsic curvature from metric and derivatives. More...
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::AA< DataType, SpatialDim, Frame >	inverse_spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::II< DataType, SpatialDim, Frame > &inverse_spatial_metric) noexcept
	Compute inverse spacetime metric from inverse spatial metric, lapse and shift. More...
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::abb< DataType, SpatialDim, Frame >	derivatives_of_spacetime_metric (const Scalar< DataType > &lapse, const Scalar< DataType > &dt_lapse, const tnsr::i< DataType, SpatialDim, Frame > &deriv_lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::I< DataType, SpatialDim, Frame > &dt_shift, const tnsr::iJ< DataType, SpatialDim, Frame > &deriv_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ii< DataType, SpatialDim, Frame > &dt_spatial_metric, const tnsr::ijj< DataType, SpatialDim, Frame > &deriv_spatial_metric) noexcept
	Computes spacetime derivative of spacetime metric from spatial metric, lapse, shift, and their space and time derivatives. More...
bool	operator!= (const KerrSchildCoords &lhs, const KerrSchildCoords &rhs) noexcept
template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType >
tnsr::aa< DataType, SpatialDim, Frame, Index >	ricci_tensor (const tnsr::Abb< DataType, SpatialDim, Frame, Index > &christoffel_2nd_kind, const tnsr::aBcc< DataType, SpatialDim, Frame, Index > &d_christoffel_2nd_kind) noexcept
	Computes Ricci tensor from the (spatial or spacetime) Christoffel symbol of the second kind and its derivative. More...
template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType >
tnsr::abb< DataType, SpatialDim, Frame, Index >	christoffel_first_kind (const tnsr::abb< DataType, SpatialDim, Frame, Index > &d_metric) noexcept
	Computes Christoffel symbol of the first kind from derivative of metric. More...
template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType >
void	christoffel_first_kind (gsl::not_null< tnsr::abb< DataType, SpatialDim, Frame, Index > *> christoffel, const tnsr::abb< DataType, SpatialDim, Frame, Index > &d_metric) noexcept
	Computes Christoffel symbol of the first kind from derivative of metric. More...
template<size_t Dim, typename Frame , typename DataType >
void	spacetime_metric (gsl::not_null< tnsr::aa< DataType, Dim, Frame > *> spacetime_metric, const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric) noexcept
	Computes the spacetime metric from the spatial metric, lapse, and shift. More...
template<size_t SpatialDim, typename Frame , typename DataType >
tnsr::aa< DataType, SpatialDim, Frame >	spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric) noexcept
	Computes the spacetime metric from the spatial metric, lapse, and shift. More...

Detailed Description

Holds functions related to general relativity.

Function Documentation

spacetime_normal_one_form()

template<size_t SpatialDim, typename Frame , typename DataType >

tnsr::a< DataType, SpatialDim, Frame > gr::spacetime_normal_one_form ( const Scalar< DataType > &  lapse )

noexcept

Computes spacetime normal one-form from lapse.

Details

If \(N\) is the lapse, then

\begin{align} n_t &= - N \\ n_i &= 0 \end{align}

is computed.