Computes the analytic data for a Linearized solution to the Bondi-Sachs equations described in [11]. More...

#include <LinearizedBondiSachs.hpp>

Classes
struct	ExtractionRadius

struct	Frequency

struct	InitialModes

Public Types
using	options = tmpl::list< InitialModes, ExtractionRadius, Frequency >

Public Types inherited from Cce::Solutions::WorldtubeData
using	creatable_classes = tmpl::list< BouncingBlackHole, GaugeWave, LinearizedBondiSachs, RobinsonTrautman, RotatingSchwarzschild, TeukolskyWave >

using	tags = tmpl::list< Tags::CauchyCartesianCoords, Tags::Dr< Tags::CauchyCartesianCoords >, gr::Tags::SpacetimeMetric< DataVector, 3 >, ::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > >, gh::Tags::Pi< DataVector, 3 >, gh::Tags::Phi< DataVector, 3 >, gr::Tags::SpatialMetric< DataVector, 3 >, ::Tags::dt< gr::Tags::SpatialMetric< DataVector, 3 > >, Tags::Dr< gr::Tags::SpatialMetric< DataVector, 3 > >, gr::Tags::Shift< DataVector, 3 >, ::Tags::dt< gr::Tags::Shift< DataVector, 3 > >, Tags::Dr< gr::Tags::Shift< DataVector, 3 > >, gr::Tags::Lapse< DataVector >, ::Tags::dt< gr::Tags::Lapse< DataVector > >, Tags::Dr< gr::Tags::Lapse< DataVector > >, Tags::News >
	The set of available tags provided by the analytic solution.

Public Member Functions
	WRAPPED_PUPable_decl_template (LinearizedBondiSachs)

	LinearizedBondiSachs (CkMigrateMessage *msg)

	LinearizedBondiSachs (const std::array< std::complex< double >, 2 > &mode_constants, double extraction_radius, double frequency)

std::unique_ptr< WorldtubeData >	get_clone () const override

void	pup (PUP::er &p) override

std::unique_ptr< Cce::InitializeJ::InitializeJ< false > >	get_initialize_j (double start_time) const 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)

virtual std::unique_ptr< WorldtubeData >	get_clone () const =0

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` More...

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 linearized solution does not have substantial shared computation to prepare before the separate component calculations. More...

void	linearized_bondi_j (gsl::not_null< SpinWeighted< ComplexDataVector, 2 > * > bondi_j, size_t l_max, double time) const
	Computes the linearized solution for \(J\). More...

void	linearized_bondi_u (gsl::not_null< SpinWeighted< ComplexDataVector, 1 > * > bondi_u, size_t l_max, double time) const
	Compute the linearized solution for \(U\). More...

void	linearized_bondi_w (gsl::not_null< SpinWeighted< ComplexDataVector, 0 > * > bondi_w, size_t l_max, double time) const
	Computes the linearized solution for \(W\). More...

void	linearized_dr_bondi_j (gsl::not_null< SpinWeighted< ComplexDataVector, 2 > * > dr_bondi_j, size_t l_max, double time) const
	Computes the linearized solution for \(\partial_r J\). More...

void	linearized_dr_bondi_u (gsl::not_null< SpinWeighted< ComplexDataVector, 1 > * > dr_bondi_u, size_t l_max, double time) const
	Compute the linearized solution for \(\partial_r U\). More...

void	linearized_dr_bondi_w (gsl::not_null< SpinWeighted< ComplexDataVector, 0 > * > dr_bondi_w, size_t l_max, double time) const
	Computes the linearized solution for \(\partial_r W\). More...

void	linearized_du_bondi_j (gsl::not_null< SpinWeighted< ComplexDataVector, 2 > * > du_bondi_j, size_t l_max, double time) const
	Computes the linearized solution for \(\partial_u J\). More...

void	linearized_du_bondi_u (gsl::not_null< SpinWeighted< ComplexDataVector, 1 > * > du_bondi_u, size_t l_max, double time) const
	Compute the linearized solution for \(\partial_u U\). More...

void	linearized_du_bondi_w (gsl::not_null< SpinWeighted< ComplexDataVector, 0 > * > du_bondi_w, size_t l_max, double time) const
	Computes the linearized solution for \(\partial_u W\). More...

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 linearized Bondi-Sachs system. More...

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 linearized Bondi-Sachs system. More...

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
	Compute the time derivative of the spherical coordinate metric from the linearized Bondi-Sachs system. More...

void	variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 > > * > news, size_t l_max, double time, tmpl::type_< Tags::News >) const override
	Determines the News function from the linearized solution parameters. More...

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
	Computes the Cartesian spacetime metric from the spherical solution provided by the derived classes. More...

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
	Computes the spatial derivatives of the Cartesian spacetime metric from the spherical solution provided by the derived classes. More...

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

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

virtual void	spherical_metric (gsl::not_null< tnsr::aa< DataVector, 3, ::Frame::Spherical<::Frame::Inertial > > * > spherical_metric, size_t l_max, double time) const =0
	Must be overriden in the derived class; should compute the spacetime metric of the analytic solution in spherical coordinates. More...

virtual 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 =0
	Must be overriden in the derived class; should compute the first radial derivative of the spacetime metric of the analytic solution in spherical coordinates. More...

virtual 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 =0
	Must be overriden in the derived class; should compute the first time derivative of the spacetime metric of the analytic solution in spherical coordinates. More...

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

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

virtual void	prepare_solution (size_t output_l_max, double time) const =0

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

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 Attributes
std::complex< double >	c_2a_ = std::numeric_limits<double>::signaling_NaN()

std::complex< double >	c_3a_ = std::numeric_limits<double>::signaling_NaN()

std::complex< double >	c_2b_ = std::numeric_limits<double>::signaling_NaN()

std::complex< double >	c_3b_ = std::numeric_limits<double>::signaling_NaN()

double	frequency_ = 0.0

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 = tuples::tagged_tuple_from_typelist< tmpl::transform< tmpl::list< Tags::CauchyCartesianCoords, Tags::Dr< Tags::CauchyCartesianCoords >, gr::Tags::SpacetimeMetric< DataVector, 3 >, gh::Tags::Pi< DataVector, 3 >, gh::Tags::Phi< DataVector, 3 >, gr::Tags::SpatialMetric< DataVector, 3 >, gr::Tags::Shift< DataVector, 3 >, gr::Tags::Lapse< DataVector >, ::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > >, ::Tags::dt< gr::Tags::SpatialMetric< DataVector, 3 > >, ::Tags::dt< gr::Tags::Shift< DataVector, 3 > >, ::Tags::dt< gr::Tags::Lapse< DataVector > >, Tags::Dr< gr::Tags::SpatialMetric< DataVector, 3 > >, Tags::Dr< gr::Tags::Shift< DataVector, 3 > >, Tags::Dr< gr::Tags::Lapse< DataVector > >, Tags::News >, tmpl::bind< IntermediateCacheTag, tmpl::_1 > > >

Detailed Description

Computes the analytic data for a Linearized solution to the Bondi-Sachs equations described in [11].

Details

The solution represented by this function is generated with only \((2,\pm2)\) and \((3,\pm3)\) modes, and is constructed according to the linearized solution documented in Section VI of [11]. For this solution, we impose additional restrictions that the linearized solution be asymptotically flat so that it is compatible with the gauge transformations performed in the SpECTRE regularity-preserving CCE. Using the notation of [11], we set:

\begin{align*} B_2 &= B_3 = 0\\ C_{2b} &= 3 C_{2a} / \nu^2\\ C_{3b} &= -3 i C_{3a} / \nu^3 \end{align*}

where \(C_{2a}\) and \(C_{3a}\) may be specified freely and are taken via input option InitialModes.

Member Function Documentation

◆ dr_spherical_metric()

void Cce::Solutions::LinearizedBondiSachs::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 linearized Bondi-Sachs system.

Details

This function dispatches to the individual computations in this class to determine the Bondi-Sachs scalars for the linearized solution. Once the scalars are determined, the radial derivative of the metric is assembled via (note \(\beta = 0\) in this solution)

\begin{align*} \partial_r g_{a b} dx^a dx^b =& - (W + r \partial_r W - 2 r h_{A B} U^A U^B - r^2 (\partial_r h_{A B}) U^A U^B - 2 r^2 h_{A B} U^A \partial_r U^B) (dt - dr)^2 \\ &- (4 r h_{A B} U^B + 2 r^2 ((\partial_r h_{A B}) U^B + h_{AB} \partial_r U^B) ) (dt - dr) dx^A + (2 r h_{A B} + r^2 \partial_r h_{A B}) dx^A dx^B, \end{align*}

where indices with capital letters refer to angular coordinates and the angular tensors may be written in terms of spin-weighted scalars. Doing so gives the metric components,

\begin{align*} \partial_r g_{t t} &= -\left( W + r \partial_r W - 2 r \Re\left(\bar J U^2 + K U \bar U\right) - r^2 \partial_r \Re\left(\bar J U^2 + K U \bar U\right)\right) \\ \partial_r g_{t r} &= -\partial_r g_{t t}\\ \partial_r g_{t \theta} &= 2 r \Re\left(K U + J \bar U\right) + r^2 \partial_r \Re\left(K U + J \bar U\right) \\ \partial_r g_{t \phi} &= 2r \Im\left(K U + J \bar U\right) + r^2 \partial_r \Im\left(K U + J \bar U\right) \\ \partial_r g_{r r} &= \partial_r g_{t t}\\ \partial_r g_{r \theta} &= -\partial_r g_{t \theta}\\ \partial_r g_{r \phi} &= -\partial_r g_{t \phi}\\ \partial_r g_{\theta \theta} &= 2 r \Re\left(J + K\right) + r^2 \Re\left(\partial_r J + \partial_r K\right) \\ \partial_r g_{\theta \phi} &= 2 r \Im\left(J\right) + r^2 \Im\left(\partial_r J\right)\\ \partial_r g_{\phi \phi} &= 2 r \Re\left(K - J\right) + r^2 \Re\left(\partial_r K - \partial_r J\right), \end{align*}

and all other components are zero.

Implements Cce::Solutions::SphericalMetricData.

◆ dt_spherical_metric()

void Cce::Solutions::LinearizedBondiSachs::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

Compute the time derivative of the spherical coordinate metric from the linearized Bondi-Sachs system.

Details

This function dispatches to the individual computations in this class to determine the Bondi-Sachs scalars for the linearized solution. Once the scalars are determined, the metric is assembled via (note \(\beta = 0\) in this solution, and note that we take coordinate \(t=u\) in converting to the Cartesian coordinates)

\begin{align*} \partial_t g_{a b} dx^a dx^b =& - (r \partial_u W - r^2 \partial_u h_{A B} U^A U^B - 2 r^2 h_{A B} U^B \partial_u U^A) (dt - dr)^2 \\ &- 2 r^2 (\partial_u h_{A B} U^B + h_{A B} \partial_u U^B) (dt - dr) dx^A + r^2 \partial_u h_{A B} dx^A dx^B, \end{align*}

where indices with capital letters refer to angular coordinates and the angular tensors may be written in terms of spin-weighted scalars. Doing so gives the metric components,

\begin{align*} \partial_t g_{t t} &= -\left(r \partial_u W - r^2 \partial_u \Re\left(\bar J U^2 + K U \bar U\right)\right)\\ \partial_t g_{t r} &= -\partial_t g_{t t}\\ \partial_t g_{t \theta} &= r^2 \partial_u \Re\left(K U + J \bar U\right)\\ \partial_t g_{t \phi} &= r^2 \partial_u \Im\left(K U + J \bar U\right)\\ \partial_t g_{r r} &= \partial_t g_{t t}\\ \partial_t g_{r \theta} &= -\partial_t g_{t \theta}\\ \partial_t g_{r \phi} &= -\partial_t g_{t \phi}\\ \partial_t g_{\theta \theta} &= r^2 \Re\left(\partial_u J + \partial_u K\right)\\ \partial_t g_{\theta \phi} &= r^2 \Im\left(\partial_u J\right)\\ \partial_t g_{\phi \phi} &= r^2 \Re\left(\partial_u K - \partial_u J\right), \end{align*}

and all other components are zero.

Implements Cce::Solutions::SphericalMetricData.

◆ get_clone()

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

overridevirtual

Implements Cce::Solutions::WorldtubeData.

◆ get_initialize_j()

std::unique_ptr< Cce::InitializeJ::InitializeJ< false > > Cce::Solutions::LinearizedBondiSachs::get_initialize_j ( double start_time ) const

overridevirtual

Reimplemented from Cce::Solutions::WorldtubeData.

◆ linearized_bondi_j()

void Cce::Solutions::LinearizedBondiSachs::linearized_bondi_j	(	gsl::not_null< SpinWeighted< ComplexDataVector, 2 > * >	bondi_j,
		size_t	l_max,
		double	time
	)		const

protected

Computes the linearized solution for \(J\).

Details

The linearized solution for \(J\) is given by [11],

\[ J = \sqrt{12} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2}) \mathrm{Re}(J_2(r) e^{i \nu u}) + \sqrt{60} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3}) \mathrm{Re}(J_3(r) e^{i \nu u}), \]

where

\begin{align*} J_2(r) &= \frac{C_{2a}}{4 r} - \frac{C_{2b}}{12 r^3}, \\ J_3(r) &= \frac{C_{3a}}{10 r} - \frac{i \nu C_{3 b}}{6 r^3} - \frac{C_{3 b}}{4 r^4}. \end{align*}

◆ linearized_bondi_u()

void Cce::Solutions::LinearizedBondiSachs::linearized_bondi_u	(	gsl::not_null< SpinWeighted< ComplexDataVector, 1 > * >	bondi_u,
		size_t	l_max,
		double	time
	)		const

protected

Compute the linearized solution for \(U\).

Details

The linearized solution for \(U\) is given by [11],

\[ U = \sqrt{3} ({}_1 Y_{2\,2} + {}_1 Y_{2\, -2}) \mathrm{Re}(U_2(r) e^{i \nu u}) + \sqrt{6} ({}_1 Y_{3\,3} - {}_1 Y_{3\, -3}) \mathrm{Re}(U_3(r) e^{i \nu u}), \]

where

\begin{align*} U_2(r) &= \frac{C_{2a}}{2 r^2} + \frac{i \nu C_{2 b}}{3 r^3} + \frac{C_{2b}}{4 r^4} \\ U_3(r) &= \frac{C_{3a}}{2 r^2} - \frac{2 \nu^2 C_{3b}}{3 r^3} + \frac{5 i \nu C_{3b}}{4 r^4} + \frac{C_{3 b}}{r^5} \end{align*}

◆ linearized_bondi_w()

void Cce::Solutions::LinearizedBondiSachs::linearized_bondi_w	(	gsl::not_null< SpinWeighted< ComplexDataVector, 0 > * >	bondi_w,
		size_t	l_max,
		double	time
	)		const

protected

Computes the linearized solution for \(W\).

Details

The linearized solution for \(W\) is given by [11],

\[ W = \frac{1}{\sqrt{2}} ({}_0 Y_{2\,2} + {}_0 Y_{2\, -2}) \mathrm{Re}(W_2(r) e^{i \nu u}) + \frac{1}{\sqrt{2}} ({}_0 Y_{3\,3} - {}_0 Y_{3\, -3}) \mathrm{Re}(W_3(r) e^{i \nu u}), \]

where

\begin{align*} W_2(r) &= - \frac{\nu^2 C_{2b}}{r^2} + \frac{i \nu C_{2 b}}{r^3} + \frac{C_{2b}}{2 r^4}, \\ W_3(r) &= -\frac{2 i \nu^3 C_{3b}}{r^2} - \frac{4 i \nu^2 C_{3b}}{r^3} + \frac{5 \nu C_{3b}}{2 r^4} + \frac{3 C_{3b}}{r^5}. \end{align*}

◆ linearized_dr_bondi_j()

void Cce::Solutions::LinearizedBondiSachs::linearized_dr_bondi_j	(	gsl::not_null< SpinWeighted< ComplexDataVector, 2 > * >	dr_bondi_j,
		size_t	l_max,
		double	time
	)		const

protected

Computes the linearized solution for \(\partial_r J\).

Details

The linearized solution for \(\partial_r J\) is given by [11],

\[ \partial_r J = \sqrt{12} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2}) \mathrm{Re}(\partial_r J_2(r) e^{i \nu u}) + \sqrt{60} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3}) \mathrm{Re}(\partial_r J_3(r) e^{i \nu u}), \]

where

\begin{align*} \partial_r J_2(r) &= - \frac{C_{2a}}{4 r^2} + \frac{C_{2b}}{4 r^4}, \\ \partial_r J_3(r) &= -\frac{C_{3a}}{10 r^2} + \frac{i \nu C_{3 b}}{2 r^4} + \frac{C_{3 b}}{r^5}. \end{align*}

◆ linearized_dr_bondi_u()

void Cce::Solutions::LinearizedBondiSachs::linearized_dr_bondi_u	(	gsl::not_null< SpinWeighted< ComplexDataVector, 1 > * >	dr_bondi_u,
		size_t	l_max,
		double	time
	)		const

protected

Compute the linearized solution for \(\partial_r U\).

Details

The linearized solution for \(\partial_r U\) is given by [11],

\[ \partial_r U = \sqrt{3} ({}_1 Y_{2\,2} + {}_1 Y_{2\, -2}) \mathrm{Re}(\partial_r U_2(r) e^{i \nu u}) + \sqrt{6} ({}_1 Y_{3\,3} - {}_1 Y_{3\, -3}) \mathrm{Re}(\partial_r U_3(r) e^{i \nu u}), \]

where

\begin{align*} \partial_r U_2(r) &= -\frac{C_{2a}}{r^3} - \frac{i \nu C_{2 b}}{r^4} - \frac{C_{2b}}{r^5} \\ \partial_r U_3(r) &= -\frac{C_{3a}}{r^3} + \frac{2 \nu^2 C_{3b}}{r^4} - \frac{5 i \nu C_{3b}}{r^5} - \frac{5 C_{3 b}}{r^6} \end{align*}

◆ linearized_dr_bondi_w()

void Cce::Solutions::LinearizedBondiSachs::linearized_dr_bondi_w	(	gsl::not_null< SpinWeighted< ComplexDataVector, 0 > * >	dr_bondi_w,
		size_t	l_max,
		double	time
	)		const

protected

Computes the linearized solution for \(\partial_r W\).

Details

The linearized solution for \(W\) is given by [11],

\[ \partial_r W = \frac{1}{\sqrt{2}} ({}_0 Y_{2\,2} + {}_0 Y_{2\, -2}) \mathrm{Re}(\partial_r W_2(r) e^{i \nu u}) + \frac{1}{\sqrt{2}} ({}_0 Y_{3\,3} - {}_0 Y_{3\, -3}) \mathrm{Re}(\partial_r W_3(r) e^{i \nu u}), \]

where

\begin{align*} \partial_r W_2(r) &= \frac{2 \nu^2 C_{2b}}{r^3} - \frac{3 i \nu C_{2 b}}{r^4} - \frac{2 C_{2b}}{r^5}, \\ \partial_r W_3(r) &= \frac{4 i \nu^3 C_{3b}}{r^3} + \frac{12 i \nu^2 C_{3b}}{r^4} - \frac{10 \nu C_{3b}}{r^5} - \frac{15 C_{3b}}{r^6}. \end{align*}

◆ linearized_du_bondi_j()

void Cce::Solutions::LinearizedBondiSachs::linearized_du_bondi_j	(	gsl::not_null< SpinWeighted< ComplexDataVector, 2 > * >	du_bondi_j,
		size_t	l_max,
		double	time
	)		const

protected

Computes the linearized solution for \(\partial_u J\).

Details

The linearized solution for \(\partial_u J\) is given by [11],

\[ \partial_u J = \sqrt{12} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2}) \mathrm{Re}(i \nu J_2(r) e^{i \nu u}) + \sqrt{60} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3}) \mathrm{Re}(i \nu J_3(r) e^{i \nu u}), \]

where

\begin{align*} J_2(r) &= \frac{C_{2a}}{4 r} - \frac{C_{2b}}{12 r^3}, \\ J_3(r) &= \frac{C_{3a}}{10 r} - \frac{i \nu C_{3 b}}{6 r^3} - \frac{C_{3 b}}{4 r^4}. \end{align*}

◆ linearized_du_bondi_u()

void Cce::Solutions::LinearizedBondiSachs::linearized_du_bondi_u	(	gsl::not_null< SpinWeighted< ComplexDataVector, 1 > * >	du_bondi_u,
		size_t	l_max,
		double	time
	)		const

protected

Compute the linearized solution for \(\partial_u U\).

Details

The linearized solution for \(U\) is given by [11],

\[ \partial_u U = \sqrt{3} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2}) \mathrm{Re}(i \nu U_2(r) e^{i \nu u}) + \sqrt{6} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3}) \mathrm{Re}(i \nu U_3(r) e^{i \nu u}), \]

where

\begin{align*} U_2(r) &= \frac{C_{2a}}{2 r^2} + \frac{i \nu C_{2 b}}{3 r^3} + \frac{C_{2b}}{4 r^4} \\ U_3(r) &= \frac{C_{3a}}{2 r^2} - \frac{2 \nu^2 C_{3b}}{3 r^3} + \frac{5 i \nu C_{3b}}{4 r^4} + \frac{C_{3 b}}{r^5} \end{align*}

◆ linearized_du_bondi_w()

void Cce::Solutions::LinearizedBondiSachs::linearized_du_bondi_w	(	gsl::not_null< SpinWeighted< ComplexDataVector, 0 > * >	du_bondi_w,
		size_t	l_max,
		double	time
	)		const

protected

Computes the linearized solution for \(\partial_u W\).

Details

The linearized solution for \(\partial_u W\) is given by [11],

\[ \partial_u W = \frac{1}{\sqrt{2}} ({}_1 Y_{2\,2} + {}_1 Y_{2\, -2}) \mathrm{Re}(i \nu W_2(r) e^{i \nu u}) + \frac{1}{\sqrt{2}} ({}_1 Y_{3\,3} - {}_1 Y_{3\, -3}) \mathrm{Re}(i \nu W_3(r) e^{i \nu u}), \]

where

\begin{align*} W_2(r) &= \frac{\nu^2 C_{2b}}{r^2} + \frac{i \nu C_{2 b}}{r^3} + \frac{C_{2b}}{2 r^4}, \\ W_3(r) &= \frac{2 i \nu^3 C_{3b}}{r^2} - \frac{4 i \nu^2 C_{3b}}{r^3} + \frac{5 \nu C_{3b}}{2 r^4} + \frac{3 C_{3b}}{r^5}. \end{align*}

◆ prepare_solution()

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

inlineoverrideprotectedvirtual

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

Implements Cce::Solutions::WorldtubeData.

◆ spherical_metric()

void Cce::Solutions::LinearizedBondiSachs::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 linearized Bondi-Sachs system.

Details

This function dispatches to the individual computations in this class to determine the Bondi-Sachs scalars for the linearized solution. Once the scalars are determined, the metric is assembled via (note \(\beta = 0\) in this solution)

\begin{align*} ds^2 =& - ((1 + r W) - r^2 h_{A B} U^A U^B) (dt - dr)^2 - 2 (dt - dr) dr \\ &- 2 r^2 h_{A B} U^B (dt - dr) dx^A + r^2 h_{A B} dx^A dx^B, \end{align*}

where indices with capital letters refer to angular coordinates and the angular tensors may be written in terms of spin-weighted scalars. Doing so gives the metric components,

\begin{align*} g_{t t} &= -\left(1 + r W - r^2 \Re\left(\bar J U^2 + K U \bar U\right)\right)\\ g_{t r} &= -1 - g_{t t}\\ g_{r r} &= 2 + g_{t t}\\ g_{t \theta} &= r^2 \Re\left(K U + J \bar U\right)\\ g_{t \phi} &= r^2 \Im\left(K U + J \bar U\right)\\ g_{r \theta} &= -g_{t \theta}\\ g_{r \phi} &= -g_{t \phi}\\ g_{\theta \theta} &= r^2 \Re\left(J + K\right)\\ g_{\theta \phi} &= r^2 \Im\left(J\right)\\ g_{\phi \phi} &= r^2 \Re\left(K - J\right), \end{align*}

and all other components are zero.

Implements Cce::Solutions::SphericalMetricData.

◆ variables_impl() [1/20]

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() [2/20]

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() [3/20]

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() [4/20]

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

overrideprotectedvirtual

Determines the News function from the linearized solution parameters.

Details

The News is determined from the formula given in [11],

\begin{align*} N = \frac{1}{2 \sqrt{3}} ({}_{-2} Y_{2\, 2} + {}_{-2} Y_{2\,-2}) \Re\left(i \nu^3 C_{2 b} e^{i \nu u}\right) + \frac{1}{\sqrt{15}} ({}_{-2} Y_{3\, 3} - {}_{-2} Y_{3\, -3}) \Re\left(- \nu^4 C_{3 b} e^{i \nu u} \right) \end{align*}

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [5/20]

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

protectedvirtual

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [6/20]

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() [7/20]

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() [8/20]

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() [9/20]

void Cce::Solutions::SphericalMetricData::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

overrideprotectedvirtual

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

Details

The derived classes provide spherical metric data via the virtual function SphericalMetricData::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().

Reimplemented from Cce::Solutions::SphericalMetricData.

◆ variables_impl() [10/20]

virtual void Cce::Solutions::WorldtubeData::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

protectedvirtual

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

Details

The derived classes provide spherical metric data via the virtual function SphericalMetricData::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().

Reimplemented from Cce::Solutions::SphericalMetricData.

◆ variables_impl() [11/20]

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() [12/20]

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() [13/20]

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() [14/20]

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() [15/20]

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() [16/20]

void Cce::Solutions::SphericalMetricData::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

overrideprotectedvirtual

Computes the spatial derivatives of the Cartesian spacetime metric from the spherical solution provided by the derived classes.

Details

The derived classes provide the radial derivative of the spherical metric data via the virtual function SphericalMetricData::dr_spherical_metric() at a resolution determined by the l_max_ argument. This function performs the additional angular derivatives necessary to assemble the full spatial derivative and performs the coordinate transformation to Cartesian coordinates via the Jacobians computed in SphericalMetricData::inverse_jacobian() and SphericalMetricData::inverse_jacobian().

Reimplemented from Cce::Solutions::SphericalMetricData.

◆ variables_impl() [17/20]

virtual void Cce::Solutions::WorldtubeData::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

protectedvirtual

Computes the spatial derivatives of the Cartesian spacetime metric from the spherical solution provided by the derived classes.

Details

The derived classes provide the radial derivative of the spherical metric data via the virtual function SphericalMetricData::dr_spherical_metric() at a resolution determined by the l_max_ argument. This function performs the additional angular derivatives necessary to assemble the full spatial derivative and performs the coordinate transformation to Cartesian coordinates via the Jacobians computed in SphericalMetricData::inverse_jacobian() and SphericalMetricData::inverse_jacobian().

Reimplemented from Cce::Solutions::SphericalMetricData.

◆ variables_impl() [18/20]

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() [19/20]

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() [20/20]

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

constexpr Options::String Cce::Solutions::LinearizedBondiSachs::help

staticconstexpr

Initial value:

{

"A linearized Bondi-Sachs analytic solution"}

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

src/Evolution/Systems/Cce/AnalyticSolutions/LinearizedBondiSachs.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()

Details

◆ get_clone()

◆ get_initialize_j()

◆ linearized_bondi_j()

Details

◆ linearized_bondi_u()

Details

◆ linearized_bondi_w()

Details

◆ linearized_dr_bondi_j()

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◆ linearized_dr_bondi_u()

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◆ linearized_dr_bondi_w()

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◆ linearized_du_bondi_j()

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◆ linearized_du_bondi_u()

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◆ linearized_du_bondi_w()

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◆ prepare_solution()

◆ spherical_metric()

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◆ variables_impl() [1/20]

◆ variables_impl() [2/20]

◆ variables_impl() [3/20]

◆ variables_impl() [4/20]

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◆ variables_impl() [5/20]

◆ variables_impl() [6/20]

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◆ variables_impl() [7/20]

◆ variables_impl() [8/20]

◆ variables_impl() [9/20]

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◆ variables_impl() [10/20]

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◆ variables_impl() [11/20]

◆ variables_impl() [12/20]

◆ variables_impl() [13/20]

◆ variables_impl() [14/20]

◆ variables_impl() [15/20]

◆ variables_impl() [16/20]

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◆ variables_impl() [17/20]

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◆ variables_impl() [18/20]

◆ variables_impl() [19/20]

◆ variables_impl() [20/20]

Member Data Documentation

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