ScalarTensor::AnalyticData::KerrSphericalHarmonic Class Reference

Analytic initial data for a pure spherical harmonic in three dimensions in a KerrSchild background. More...

#include <KerrSphericalHarmonic.hpp>

Classes
struct	Amplitude
	The amplitude of the scalar field. More...
struct	Mass
	The mass of the black hole. More...
struct	Mode
	The spherical harmonic mode of the scalar field. More...
struct	Radius
	The location of the scalar field. More...
struct	Spin
	The spin of the black hole. More...
struct	Width
	The width of the scalar field. More...

Public Types
using	options = tmpl::list< Mass, Spin, Amplitude, Radius, Width, Mode >
template<typename DataType , typename Frame = Frame::Inertial>
using	tags = tmpl::flatten< tmpl::list< typename AnalyticDataBase::template tags< DataType >, gr::Tags::DerivDetSpatialMetric< DataType, 3, Frame >, gr::Tags::TraceExtrinsicCurvature< DataType >, gr::Tags::SpatialChristoffelFirstKind< DataType, 3, Frame >, gr::Tags::SpatialChristoffelSecondKind< DataType, 3, Frame >, gr::Tags::TraceSpatialChristoffelSecondKind< DataType, 3, Frame > > >
Public Types inherited from ScalarTensor::AnalyticDataBase
template<typename DataType >
using	tags = tmpl::push_back< typename gr::AnalyticDataBase< volume_dim >::template tags< DataType >, CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi, CurvedScalarWave::Tags::Phi< volume_dim > >

Public Member Functions
	KerrSphericalHarmonic (const KerrSphericalHarmonic &)=default
KerrSphericalHarmonic &	operator= (const KerrSphericalHarmonic &)=default
	KerrSphericalHarmonic (KerrSphericalHarmonic &&)=default
KerrSphericalHarmonic &	operator= (KerrSphericalHarmonic &&)=default
	KerrSphericalHarmonic (double mass, const std::array< double, 3 > &dimensionless_spin, double amplitude, double radius, double width, std::pair< size_t, int > mode)
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tags... >) const
	Retrieve a collection of scalar variables at x
template<typename DataType , typename Tag >
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag >) const
	Retrieve the metric variables.
void	pup (PUP::er &) override
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< CurvedScalarWave::Tags::Psi >) const -> tuples::TaggedTuple< CurvedScalarWave::Tags::Psi >
	Retrieve scalar variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< CurvedScalarWave::Tags::Phi< 3_st > >) const -> tuples::TaggedTuple< CurvedScalarWave::Tags::Phi< 3_st > >
	Retrieve scalar variable at x
template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< CurvedScalarWave::Tags::Pi >) const -> tuples::TaggedTuple< CurvedScalarWave::Tags::Pi >
	Retrieve scalar variable at x
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr Options::String	help
Static Public Attributes inherited from ScalarTensor::AnalyticDataBase
static constexpr size_t	volume_dim = 3_st

Protected Attributes
double	mass_ = std::numeric_limits<double>::signaling_NaN()
std::array< double, volume_dim >	dimensionless_spin_
double	amplitude_ = std::numeric_limits<double>::signaling_NaN()
double	radius_ {std::numeric_limits<double>::signaling_NaN()}
double	width_sq_ {std::numeric_limits<double>::signaling_NaN()}
std::pair< size_t, int >	mode_
gr::Solutions::KerrSchild	background_spacetime_ {}

Friends
bool	operator== (const KerrSphericalHarmonic &lhs, const KerrSphericalHarmonic &rhs)

Detailed Description

Analytic initial data for a pure spherical harmonic in three dimensions in a KerrSchild background.

Details

The initial data is taken from [162] , Eqs. 4.1–4.3, and sets the evolved variables of the scalar wave as follows:

\begin{align} \Psi &= 0 \\ \Phi_i &= 0 \\ \Pi &= \Pi_0(r, \theta, \phi) = A e^{- (r - r_0)^2 / w^2} Y_{lm}(\theta, \phi), \end{align}

where \(A\) is the amplitude of the profile, \(r_0\) is its radius and \(w\) is its width. This describes a pure spherical harmonic mode \(Y_{lm}(\theta, \phi)\) truncated by a circular Gaussian window function.

When evolved, the scalar field \(\Phi\) will briefly build up around the radius \(r_0\) and then disperse. This can be used to study the ringdown behavior and late-time tails in the Kerr spacetime.

See also

CurvedScalarWave::AnalyticData::PureSphericalHarmonic and gr::Solutions::KerrSchild.

Member Function Documentation

get_clone()

auto ScalarTensor::AnalyticData::KerrSphericalHarmonic::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

dimensionless_spin_

std::array<double, volume_dim> ScalarTensor::AnalyticData::KerrSphericalHarmonic::dimensionless_spin_

protected

Initial value:

=
      make_array<volume_dim>(std::numeric_limits<double>::signaling_NaN())

help

constexpr Options::String ScalarTensor::AnalyticData::KerrSphericalHarmonic::help

staticconstexpr

Initial value:

= {
      "Initial data for a pure spherical harmonic mode truncated by a circular "
      "Gaussian window funtion. The expression is taken from Scheel(2003), "
      "equations 4.1-4.3."}

mode_

std::pair<size_t, int> ScalarTensor::AnalyticData::KerrSphericalHarmonic::mode_

protected

Initial value:

{std::numeric_limits<size_t>::signaling_NaN(),
                               std::numeric_limits<int>::signaling_NaN()}

---

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

• src/PointwiseFunctions/AnalyticData/ScalarTensor/KerrSphericalHarmonic.hpp