Classes | Public Types | Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes | List of all members
Cce::Solutions::RotatingSchwarzschild Struct Reference

Computes the analytic data for the rotating Schwarzschild solution described in [7], 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 = tmpl::list< BouncingBlackHole, GaugeWave, LinearizedBondiSachs, RobinsonTrautman, RotatingSchwarzschild, TeukolskyWave >
 
using tags = tmpl::list< Tags::CauchyCartesianCoords, Tags::Dr< Tags::CauchyCartesianCoords >, gr::Tags::SpacetimeMetric< 3, ::Frame::Inertial, DataVector >, ::Tags::dt< gr::Tags::SpacetimeMetric< 3, ::Frame::Inertial, DataVector > >, GeneralizedHarmonic::Tags::Pi< 3, ::Frame::Inertial >, GeneralizedHarmonic::Tags::Phi< 3, ::Frame::Inertial >, gr::Tags::SpatialMetric< 3, ::Frame::Inertial, DataVector >, ::Tags::dt< gr::Tags::SpatialMetric< 3, ::Frame::Inertial, DataVector > >, Tags::Dr< gr::Tags::SpatialMetric< 3, ::Frame::Inertial, DataVector > >, gr::Tags::Shift< 3, ::Frame::Inertial, DataVector >, ::Tags::dt< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector > >, Tags::Dr< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector > >, 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 (RotatingSchwarzschild)
 
 RotatingSchwarzschild (CkMigrateMessage *msg) noexcept
 
 RotatingSchwarzschild (double extraction_radius, double mass, double frequency) noexcept
 
std::unique_ptr< WorldtubeDataget_clone () const noexcept override
 
void pup (PUP::er &p) noexcept override
 
- Public Member Functions inherited from Cce::Solutions::SphericalMetricData
 WRAPPED_PUPable_abstract (SphericalMetricData)
 
 SphericalMetricData (CkMigrateMessage *msg) noexcept
 
 SphericalMetricData (const double extraction_radius) noexcept
 
void jacobian (gsl::not_null< SphericaliCartesianJ * > jacobian, size_t l_max) const noexcept
 
void inverse_jacobian (gsl::not_null< CartesianiSphericalJ * > inverse_jacobian, size_t l_max) const noexcept
 
void dr_inverse_jacobian (gsl::not_null< CartesianiSphericalJ * > dr_inverse_jacobian, size_t l_max) const noexcept
 
void pup (PUP::er &p) noexcept override
 
- Public Member Functions inherited from Cce::Solutions::WorldtubeData
 WRAPPED_PUPable_abstract (WorldtubeData)
 
 WorldtubeData (const double extraction_radius) noexcept
 
 WorldtubeData (CkMigrateMessage *msg) noexcept
 
template<typename... Tags>
tuples::TaggedTuple< Tags... > variables (const size_t output_l_max, const double time, tmpl::list< Tags... >) const noexcept
 Retrieve worldtube data represented by the analytic solution, at boundary angular resolution l_max and time time More...
 
void pup (PUP::er &p) noexcept override
 
virtual std::unique_ptr< Cce::InitializeJ::InitializeJget_initialize_j (const double) const noexcept
 
virtual bool use_noninertial_news () const noexcept
 

Static Public Attributes

static constexpr Options::String help
 

Protected Member Functions

void prepare_solution (const size_t, const double) const noexcept 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 noexcept override
 Compute the spherical coordinate metric from the closed-form rotating Schwarzschild metric. 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 noexcept override
 Compute the radial derivative of the spherical coordinate metric from the closed-form rotating Schwarzschild metric. 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 noexcept 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 noexcept 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 noexcept
 
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 noexcept
 
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< 3, ::Frame::Inertial, DataVector >>) const noexcept=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< 3, ::Frame::Inertial, DataVector >>>) const noexcept=0
 
virtual void variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > pi, size_t output_l_max, double time, tmpl::type_< GeneralizedHarmonic::Tags::Pi< 3, ::Frame::Inertial >>) const noexcept
 
virtual void variables_impl (gsl::not_null< tnsr::iaa< DataVector, 3 > * > d_spacetime_metric, size_t output_l_max, double time, tmpl::type_< GeneralizedHarmonic::Tags::Phi< 3, ::Frame::Inertial >>) const noexcept=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< 3, ::Frame::Inertial, DataVector >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
virtual void variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > shift, size_t output_l_max, double time, tmpl::type_< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
virtual void variables_impl (gsl::not_null< Scalar< DataVector > * > lapse, size_t output_l_max, double time, tmpl::type_< gr::Tags::Lapse< DataVector >>) const noexcept
 
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 noexcept
 
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 noexcept
 
virtual void variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 >> * > news, size_t output_l_max, double time, tmpl::type_< Tags::News >) const noexcept=0
 
void variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > spacetime_metric, size_t l_max, double time, tmpl::type_< gr::Tags::SpacetimeMetric< 3, ::Frame::Inertial, DataVector >>) const noexcept 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< 3, ::Frame::Inertial, DataVector >>>) const noexcept 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_< GeneralizedHarmonic::Tags::Phi< 3, ::Frame::Inertial >>) const noexcept 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< 3, ::Frame::Inertial, DataVector >>) const noexcept 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< 3, ::Frame::Inertial, DataVector >>>) const noexcept 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_< GeneralizedHarmonic::Tags::Phi< 3, ::Frame::Inertial >>) const noexcept override
 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::i< DataVector, 3 > * > cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::CauchyCartesianCoords >) const noexcept
 
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 noexcept
 
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< 3, ::Frame::Inertial, DataVector >>) const noexcept=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< 3, ::Frame::Inertial, DataVector >>>) const noexcept=0
 
virtual void variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > pi, size_t output_l_max, double time, tmpl::type_< GeneralizedHarmonic::Tags::Pi< 3, ::Frame::Inertial >>) const noexcept
 
virtual void variables_impl (gsl::not_null< tnsr::iaa< DataVector, 3 > * > d_spacetime_metric, size_t output_l_max, double time, tmpl::type_< GeneralizedHarmonic::Tags::Phi< 3, ::Frame::Inertial >>) const noexcept=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< 3, ::Frame::Inertial, DataVector >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
virtual void variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > shift, size_t output_l_max, double time, tmpl::type_< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
virtual void variables_impl (gsl::not_null< Scalar< DataVector > * > lapse, size_t output_l_max, double time, tmpl::type_< gr::Tags::Lapse< DataVector >>) const noexcept
 
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 noexcept
 
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 noexcept
 
virtual void variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 >> * > news, size_t output_l_max, double time, tmpl::type_< Tags::News >) const noexcept=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 noexcept
 
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 noexcept
 
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 noexcept
 
virtual void variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > pi, size_t output_l_max, double time, tmpl::type_< GeneralizedHarmonic::Tags::Pi< 3, ::Frame::Inertial >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
virtual void variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > shift, size_t output_l_max, double time, tmpl::type_< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector >>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
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< 3, ::Frame::Inertial, DataVector >>>) const noexcept
 
virtual void variables_impl (gsl::not_null< Scalar< DataVector > * > lapse, size_t output_l_max, double time, tmpl::type_< gr::Tags::Lapse< DataVector >>) const noexcept
 
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 noexcept
 
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 noexcept
 

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) noexcept
 
- 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< 3, ::Frame::Inertial, DataVector >, GeneralizedHarmonic::Tags::Pi< 3, ::Frame::Inertial >, GeneralizedHarmonic::Tags::Phi< 3, ::Frame::Inertial >, gr::Tags::SpatialMetric< 3, ::Frame::Inertial, DataVector >, gr::Tags::Shift< 3, ::Frame::Inertial, DataVector >, gr::Tags::Lapse< DataVector >, ::Tags::dt< gr::Tags::SpacetimeMetric< 3, ::Frame::Inertial, DataVector > >, ::Tags::dt< gr::Tags::SpatialMetric< 3, ::Frame::Inertial, DataVector > >, ::Tags::dt< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector > >, ::Tags::dt< gr::Tags::Lapse< DataVector > >, Tags::Dr< gr::Tags::SpatialMetric< 3, ::Frame::Inertial, DataVector > >, Tags::Dr< gr::Tags::Shift< 3, ::Frame::Inertial, DataVector > >, Tags::Dr< gr::Tags::Lapse< DataVector > >, Tags::News >, tmpl::bind< IntermediateCacheTag, tmpl::_1 > >>
 

Detailed Description

Computes the analytic data for the rotating Schwarzschild solution described in [7], 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
overrideprotectedvirtualnoexcept

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

Details

The rotating Schwarzschild takes the coordinate form [7],

\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.

◆ 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
overrideprotectedvirtualnoexcept

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

Details

The rotating Schwarzschild takes the coordinate form [7],

\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() [1/3]

void Cce::Solutions::SphericalMetricData::variables_impl
overrideprotectednoexcept

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() [2/3]

void Cce::Solutions::SphericalMetricData::variables_impl
overrideprotectednoexcept

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().

◆ variables_impl() [3/3]

void Cce::Solutions::SphericalMetricData::variables_impl
overrideprotectednoexcept

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().

Member Data Documentation

◆ help

constexpr 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: