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Cce::Solutions::BouncingBlackHole Struct Reference

Analytic solution representing a coordinate oscillation about a stationary Schwarzschild black hole. More...

#include <BouncingBlackHole.hpp>

Classes

struct  Amplitude
 
struct  ExtractionRadius
 
struct  Mass
 
struct  Period
 

Public Types

using options = tmpl::list< Amplitude, ExtractionRadius, Mass, Period >
 
- 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 (BouncingBlackHole)
 
 BouncingBlackHole (CkMigrateMessage *msg) noexcept
 
 BouncingBlackHole (double amplitude, double extraction_radius, double mass, double period) noexcept
 
std::unique_ptr< WorldtubeDataget_clone () const noexcept override
 
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
 
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
 The implementation function that computes the spacetime metric on the extraction sphere at collocation points associated with angular resolution l_max. 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
 The implementation function that computes the first time derivative of the spacetime metric on the extraction sphere. 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
 The implementation function that computes the first spatial derivative of the spacetime metric on the extraction sphere. More...
 
void variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 >> * > news, size_t output_l_max, double time, tmpl::type_< Tags::News >) const noexcept override
 The News in the bouncing black hole solution vanishes, as the oscillation comes entirely from a coordinate transform.
 
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 amplitude_ = std::numeric_limits<double>::signaling_NaN()
 
double mass_ = std::numeric_limits<double>::signaling_NaN()
 
double frequency_ = 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

- 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

Analytic solution representing a coordinate oscillation about a stationary Schwarzschild black hole.

Details

As the oscillation in the metric data at the worldtube is a pure coordinate effect, the system evolved using this worldtube data should produce zero news. The solution is a coordinate transform applied to the Schwarzschild solution in Kerr-Schild coordinates.

Member Function Documentation

◆ variables_impl() [1/3]

void Cce::Solutions::BouncingBlackHole::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
overrideprotectedvirtualnoexcept

The implementation function that computes the first time derivative of the spacetime metric on the extraction sphere.

Details

The time derivative of the spacetime metric \(\partial_t g_{a b}\) comes entirely from the Jacobian factor:

\begin{align*} \partial_t x = \frac{8 \pi A}{T} \cos\left(\frac{2 \pi t}{T}\right) \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^3, \end{align*}

so the transformed metric derivative is,

\begin{align*} \partial_t g_{a^\prime b^\prime} = 2 \partial_{(a^\prime} \partial_t x \partial_{b^\prime)} x^a g_{x a}. \end{align*}

In this notation we take the primed coordinates to be the coordinates for which the black hole has time-dependent coordinate position.

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [2/3]

void Cce::Solutions::BouncingBlackHole::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
overrideprotectedvirtualnoexcept

The implementation function that computes the spacetime metric on the extraction sphere at collocation points associated with angular resolution l_max.

Details

The spacetime metric \(g_{a b}\) is determined by evaluating the Kerr-Schild metric at a set of transformed coordinates \(t^\prime = t, y^\prime = y, z^\prime = z\), and

\begin{align*} x = x^\prime + A \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^4, \end{align*}

where the amplitude \(A\) is set by the option Amplitude and the period \(T\) is set by the option Period. In this notation we take the primed coordinates to be the coordinates for which the black hole has time-dependent coordinate position.

Implements Cce::Solutions::WorldtubeData.

◆ variables_impl() [3/3]

void Cce::Solutions::BouncingBlackHole::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
overrideprotectedvirtualnoexcept

The implementation function that computes the first spatial derivative of the spacetime metric on the extraction sphere.

Details

The calculation proceeds by standard coordinate transform techniques for the transformation given by \(t^\prime = t, y^\prime = y, z^\prime = z\), and

\begin{align*} x = x^\prime + A \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^4, \end{align*}

The general coordinate transformation formula that gives the metric is then

\begin{align*} \partial_a g_{b c} = \partial_a \partial_b x^{\prime a^\prime} \partial_c x^{\prime b^\prime} g_{a^\prime b^\prime} + \partial_b x^{\prime a^\prime} \partial_a \partial_c x^{\prime b^\prime} g_{a^\prime b^\prime} + \partial_a x^{\prime a^\prime} \partial_b x^{\prime b^\prime} \partial_c x^{\prime c^\prime} \partial_a g_{b c} \end{align*}

Implements Cce::Solutions::WorldtubeData.

Member Data Documentation

◆ help

constexpr Options::String Cce::Solutions::BouncingBlackHole::help
staticconstexpr
Initial value:
{
"Analytic solution in which a static black hole is placed in an "
"oscillating coordinate system"}

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