Computes the analytic data for the rotating Schwarzschild solution described in [11], section VI.C. More...

#include <RotatingSchwarzschild.hpp>

Classes
struct	ExtractionRadius
struct	Frequency
struct	Mass

Public Types
using	options = tmpl::list<ExtractionRadius, Mass, Frequency>
Public Types inherited from Cce::Solutions::WorldtubeData
using	creatable_classes
using	tags
	The set of available tags provided by the analytic solution.

Public Member Functions
	WRAPPED_PUPable_decl_template (RotatingSchwarzschild)
	RotatingSchwarzschild (CkMigrateMessage *msg)
	RotatingSchwarzschild (double extraction_radius, double mass, double frequency)
std::unique_ptr< WorldtubeData >	get_clone () const override
void	pup (PUP::er &p) override
Public Member Functions inherited from Cce::Solutions::SphericalMetricData
	WRAPPED_PUPable_abstract (SphericalMetricData)
	SphericalMetricData (CkMigrateMessage *msg)
	SphericalMetricData (const double extraction_radius)
void	jacobian (gsl::not_null< SphericaliCartesianJ * > jacobian, size_t l_max) const
void	inverse_jacobian (gsl::not_null< CartesianiSphericalJ * > inverse_jacobian, size_t l_max) const
void	dr_inverse_jacobian (gsl::not_null< CartesianiSphericalJ * > dr_inverse_jacobian, size_t l_max) const
void	pup (PUP::er &p) override
Public Member Functions inherited from Cce::Solutions::WorldtubeData
	WRAPPED_PUPable_abstract (WorldtubeData)
	WorldtubeData (const double extraction_radius)
	WorldtubeData (CkMigrateMessage *msg)
template<typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const size_t output_l_max, const double time, tmpl::list< Tags... >) const
	Retrieve worldtube data represented by the analytic solution, at boundary angular resolution l_max and time time
void	pup (PUP::er &p) override
virtual std::unique_ptr< Cce::InitializeJ::InitializeJ< false > >	get_initialize_j (const double) const
virtual bool	use_noninertial_news () const

Static Public Attributes
static constexpr Options::String	help

Protected Member Functions
void	prepare_solution (const size_t, const double) const override
	A no-op as the rotating Schwarzschild solution does not have substantial shared computation to prepare before the separate component calculations.
void	spherical_metric (gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * > spherical_metric, size_t l_max, double time) const override
	Compute the spherical coordinate metric from the closed-form rotating Schwarzschild metric.
void	dr_spherical_metric (gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * > dr_spherical_metric, size_t l_max, double time) const override
	Compute the radial derivative of the spherical coordinate metric from the closed-form rotating Schwarzschild metric.
void	dt_spherical_metric (gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * > dt_spherical_metric, size_t l_max, double time) const override
	The time derivative of the spherical coordinate metric in the rotating Schwarzschild metric vanishes.
void	variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 > > * > news, size_t l_max, double time, tmpl::type_< Tags::News >) const override
	The News vanishes in the rotating Schwarzschild metric.
virtual void	variables_impl (gsl::not_null< tnsr::i< DataVector, 3 > * > cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::CauchyCartesianCoords >) const
virtual void	variables_impl (gsl::not_null< tnsr::i< DataVector, 3 > * > dr_cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::Dr< Tags::CauchyCartesianCoords > >) const
virtual void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > spacetime_metric, size_t output_l_max, double time, tmpl::type_< gr::Tags::SpacetimeMetric< DataVector, 3 > >) const=0
virtual void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > dt_spacetime_metric, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >) const=0
virtual void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > pi, size_t output_l_max, double time, tmpl::type_< gh::Tags::Pi< DataVector, 3 > >) const
virtual void	variables_impl (gsl::not_null< tnsr::iaa< DataVector, 3 > * > d_spacetime_metric, size_t output_l_max, double time, tmpl::type_< gh::Tags::Phi< DataVector, 3 > >) const=0
virtual void	variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > spatial_metric, size_t output_l_max, double time, tmpl::type_< gr::Tags::SpatialMetric< DataVector, 3 > >) const
virtual void	variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > dt_spatial_metric, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::SpatialMetric< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > dr_spatial_metric, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::SpatialMetric< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > shift, size_t output_l_max, double time, tmpl::type_< gr::Tags::Shift< DataVector, 3 > >) const
virtual void	variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > dt_shift, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::Shift< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > dr_shift, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::Shift< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< Scalar< DataVector > * > lapse, size_t output_l_max, double time, tmpl::type_< gr::Tags::Lapse< DataVector > >) const
virtual void	variables_impl (gsl::not_null< Scalar< DataVector > * > dt_lapse, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::Lapse< DataVector > > >) const
virtual void	variables_impl (gsl::not_null< Scalar< DataVector > * > dr_lapse, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::Lapse< DataVector > > >) const
void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > dt_spacetime_metric, size_t l_max, double time, tmpl::type_< ::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >) const override
	Computes the time derivative of the Cartesian spacetime metric from the spherical solution provided by the derived classes.
Protected Member Functions inherited from Cce::Solutions::SphericalMetricData
void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > spacetime_metric, size_t l_max, double time, tmpl::type_< gr::Tags::SpacetimeMetric< DataVector, 3 > >) const override
	Computes the Cartesian spacetime metric from the spherical solution provided by the derived classes.
void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > dt_spacetime_metric, size_t l_max, double time, tmpl::type_< ::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >) const override
	Computes the time derivative of the Cartesian spacetime metric from the spherical solution provided by the derived classes.
void	variables_impl (gsl::not_null< tnsr::iaa< DataVector, 3 > * > d_spacetime_metric, size_t l_max, double time, tmpl::type_< gh::Tags::Phi< DataVector, 3 > >) const override
	Computes the spatial derivatives of the Cartesian spacetime metric from the spherical solution provided by the derived classes.
virtual void	variables_impl (gsl::not_null< tnsr::i< DataVector, 3 > * > cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::CauchyCartesianCoords >) const
virtual void	variables_impl (gsl::not_null< tnsr::i< DataVector, 3 > * > dr_cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::Dr< Tags::CauchyCartesianCoords > >) const
virtual void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > dt_spacetime_metric, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >) const=0
virtual void	variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > pi, size_t output_l_max, double time, tmpl::type_< gh::Tags::Pi< DataVector, 3 > >) const
virtual void	variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > spatial_metric, size_t output_l_max, double time, tmpl::type_< gr::Tags::SpatialMetric< DataVector, 3 > >) const
virtual void	variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > dt_spatial_metric, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::SpatialMetric< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > dr_spatial_metric, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::SpatialMetric< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > shift, size_t output_l_max, double time, tmpl::type_< gr::Tags::Shift< DataVector, 3 > >) const
virtual void	variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > dt_shift, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::Shift< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > dr_shift, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::Shift< DataVector, 3 > > >) const
virtual void	variables_impl (gsl::not_null< Scalar< DataVector > * > lapse, size_t output_l_max, double time, tmpl::type_< gr::Tags::Lapse< DataVector > >) const
virtual void	variables_impl (gsl::not_null< Scalar< DataVector > * > dt_lapse, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::Lapse< DataVector > > >) const
virtual void	variables_impl (gsl::not_null< Scalar< DataVector > * > dr_lapse, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::Lapse< DataVector > > >) const
virtual void	variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 > > * > news, size_t output_l_max, double time, tmpl::type_< Tags::News >) const=0
Protected Member Functions inherited from Cce::Solutions::WorldtubeData
template<typename Tag>
const auto &	cache_or_compute (const size_t output_l_max, const double time) const

Protected Attributes
double	frequency_ = std::numeric_limits<double>::signaling_NaN()
double	mass_ = std::numeric_limits<double>::signaling_NaN()
Protected Attributes inherited from Cce::Solutions::WorldtubeData
IntermediateCacheTuple	intermediate_cache_
double	extraction_radius_ = std::numeric_limits<double>::quiet_NaN()

Additional Inherited Members
Static Public Member Functions inherited from Cce::Solutions::SphericalMetricData
static void	dr_jacobian (gsl::not_null< SphericaliCartesianJ * > dr_jacobian, size_t l_max)
Protected Types inherited from Cce::Solutions::WorldtubeData
using	IntermediateCacheTuple

Detailed Description

Computes the analytic data for the rotating Schwarzschild solution described in [11], section VI.C.

Details

This is a comparatively simple test which simply determines the Schwarzschild metric in transformed coordinates given by \(\phi\rightarrow \phi + \omega u\), where \(u\) is the retarded time.

Member Function Documentation

◆ dr_spherical_metric()

void Cce::Solutions::RotatingSchwarzschild::dr_spherical_metric	(	gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * >	dr_spherical_metric,
		size_t	l_max,
		double	time ) const

overrideprotectedvirtual

Compute the radial derivative of the spherical coordinate metric from the closed-form rotating Schwarzschild metric.

Details

The rotating Schwarzschild takes the coordinate form [11],

\begin{align}\partial_r g_{a b} dx^a dx^b =& -\left(\frac{2 M}{r^2} - 2 \omega^2 r \sin^2 \theta\right) dt^2 - \frac{2 M}{(r - 2 M)^2} dr^2 + 4 \omega r \sin^2 \theta dt d\phi + 2 r d\Omega^2 \end{align}

Implements Cce::Solutions::SphericalMetricData.

◆ dt_spherical_metric()

void Cce::Solutions::RotatingSchwarzschild::dt_spherical_metric	(	gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * >	dt_spherical_metric,
		size_t	l_max,
		double	time ) const

overrideprotectedvirtual

The time derivative of the spherical coordinate metric in the rotating Schwarzschild metric vanishes.

Implements Cce::Solutions::SphericalMetricData.

◆ get_clone()

std::unique_ptr< WorldtubeData > Cce::Solutions::RotatingSchwarzschild::get_clone ( ) const

overridevirtual

Implements Cce::Solutions::WorldtubeData.

◆ prepare_solution()

void Cce::Solutions::RotatingSchwarzschild::prepare_solution	(	const size_t	,
		const double	) const

inlineoverrideprotectedvirtual

A no-op as the rotating Schwarzschild solution does not have substantial shared computation to prepare before the separate component calculations.

Implements Cce::Solutions::WorldtubeData.

◆ spherical_metric()

void Cce::Solutions::RotatingSchwarzschild::spherical_metric	(	gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * >	spherical_metric,
		size_t	l_max,
		double	time ) const

overrideprotectedvirtual

Compute the spherical coordinate metric from the closed-form rotating Schwarzschild metric.

Details

The rotating Schwarzschild takes the coordinate form [11],

\begin{align}ds^2 = -\left(1 - \frac{2 M}{r} - \omega^2 r^2 \sin^2 \theta\right) dt^2 + \frac{1}{1 - \frac{2 M}{r}} dr^2 + 2 \omega r^2 \sin^2 \theta dt d\phi + r^2 d\Omega^2 \end{align}

Implements Cce::Solutions::SphericalMetricData.

◆ variables_impl() [1/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< Scalar< DataVector > * >	dr_lapse,
		size_t	output_l_max,
		double	time,
		tmpl::type_< Tags::Dr< gr::Tags::Lapse< DataVector > > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [2/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< Scalar< DataVector > * >	dt_lapse,
		size_t	output_l_max,
		double	time,
		tmpl::type_<::Tags::dt< gr::Tags::Lapse< DataVector > > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [3/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< Scalar< DataVector > * >	lapse,
		size_t	output_l_max,
		double	time,
		tmpl::type_< gr::Tags::Lapse< DataVector > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [4/17]

void Cce::Solutions::RotatingSchwarzschild::variables_impl	(	gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 > > * >	news,
		size_t	l_max,
		double	time,
		tmpl::type_< Tags::News >	) const

overrideprotectedvirtual

The News vanishes in the rotating Schwarzschild metric.

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [5/17]

void Cce::Solutions::SphericalMetricData::variables_impl	(	gsl::not_null< tnsr::aa< DataVector, 3 > * >	dt_spacetime_metric,
		size_t	l_max,
		double	time,
		tmpl::type_< ::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >	) const

overrideprotected

Computes the time derivative of the Cartesian spacetime metric from the spherical solution provided by the derived classes.

Details

The derived classes provide the time derivative of the spherical metric data via the virtual function SphericalMetricData::dt_spherical_metric() at a resolution determined by the l_max argument. This function performs the coordinate transformation using the Jacobian computed from SphericalMetricData::inverse_jacobian().

◆ variables_impl() [6/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::aa< DataVector, 3 > * >	dt_spacetime_metric,
		size_t	output_l_max,
		double	time,
		tmpl::type_<::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >	) const

protectedvirtual

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [7/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::aa< DataVector, 3 > * >	pi,
		size_t	output_l_max,
		double	time,
		tmpl::type_< gh::Tags::Pi< DataVector, 3 > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [8/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::aa< DataVector, 3 > * >	spacetime_metric,
		size_t	output_l_max,
		double	time,
		tmpl::type_< gr::Tags::SpacetimeMetric< DataVector, 3 > >	) const

protectedvirtual

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [9/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::i< DataVector, 3 > * >	cartesian_coordinates,
		size_t	output_l_max,
		double	time,
		tmpl::type_< Tags::CauchyCartesianCoords >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [10/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::i< DataVector, 3 > * >	dr_cartesian_coordinates,
		size_t	output_l_max,
		double	time,
		tmpl::type_< Tags::Dr< Tags::CauchyCartesianCoords > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [11/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::I< DataVector, 3 > * >	dr_shift,
		size_t	output_l_max,
		double	time,
		tmpl::type_< Tags::Dr< gr::Tags::Shift< DataVector, 3 > > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [12/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::I< DataVector, 3 > * >	dt_shift,
		size_t	output_l_max,
		double	time,
		tmpl::type_<::Tags::dt< gr::Tags::Shift< DataVector, 3 > > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [13/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::I< DataVector, 3 > * >	shift,
		size_t	output_l_max,
		double	time,
		tmpl::type_< gr::Tags::Shift< DataVector, 3 > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [14/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::iaa< DataVector, 3 > * >	d_spacetime_metric,
		size_t	output_l_max,
		double	time,
		tmpl::type_< gh::Tags::Phi< DataVector, 3 > >	) const

protectedvirtual

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [15/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::ii< DataVector, 3 > * >	dr_spatial_metric,
		size_t	output_l_max,
		double	time,
		tmpl::type_< Tags::Dr< gr::Tags::SpatialMetric< DataVector, 3 > > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [16/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::ii< DataVector, 3 > * >	dt_spatial_metric,
		size_t	output_l_max,
		double	time,
		tmpl::type_<::Tags::dt< gr::Tags::SpatialMetric< DataVector, 3 > > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ variables_impl() [17/17]

virtual void Cce::Solutions::WorldtubeData::variables_impl	(	gsl::not_null< tnsr::ii< DataVector, 3 > * >	spatial_metric,
		size_t	output_l_max,
		double	time,
		tmpl::type_< gr::Tags::SpatialMetric< DataVector, 3 > >	) const

protectedvirtual

Reimplemented from Cce::Solutions::WorldtubeData.

Member Data Documentation

◆ help

Options::String Cce::Solutions::RotatingSchwarzschild::help

staticconstexpr

Initial value:

= {
      "Analytic solution representing a Schwarzschild black hole in a rotating "
      "frame"}

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

src/Evolution/Systems/Cce/AnalyticSolutions/RotatingSchwarzschild.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Details

Member Function Documentation

◆ dr_spherical_metric()

Details

◆ dt_spherical_metric()

◆ get_clone()

◆ prepare_solution()

◆ spherical_metric()

Details

◆ variables_impl() [1/17]

◆ variables_impl() [2/17]

◆ variables_impl() [3/17]

◆ variables_impl() [4/17]

◆ variables_impl() [5/17]

Details

◆ variables_impl() [6/17]

◆ variables_impl() [7/17]

◆ variables_impl() [8/17]

◆ variables_impl() [9/17]

◆ variables_impl() [10/17]

◆ variables_impl() [11/17]

◆ variables_impl() [12/17]

◆ variables_impl() [13/17]

◆ variables_impl() [14/17]

◆ variables_impl() [15/17]

◆ variables_impl() [16/17]

◆ variables_impl() [17/17]

Member Data Documentation

◆ help