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

#include <PureSphericalHarmonic.hpp>

Classes
struct	Mode
struct	Radius
struct	Width

Public Types
using	options = tmpl::list<Radius, Width, Mode>
using	tags

Public Member Functions
	PureSphericalHarmonic (double radius, double width, std::pair< size_t, int > mode, const Options::Context &context={})
	PureSphericalHarmonic (const PureSphericalHarmonic &)=default
PureSphericalHarmonic &	operator= (const PureSphericalHarmonic &)=default
	PureSphericalHarmonic (PureSphericalHarmonic &&)=default
PureSphericalHarmonic &	operator= (PureSphericalHarmonic &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
tuples::TaggedTuple< CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi, CurvedScalarWave::Tags::Phi< 3 > >	variables (const tnsr::I< DataVector, 3 > &x, tags) const
	Retrieve the evolution variables at spatial coordinates x
void	pup (PUP::er &) override
Public Member Functions inherited from evolution::initial_data::InitialData
virtual const InitialData &	unwrap () const
	Unwrap wrapper types (e.g. WithNoise, which wraps analytic initial data and adds random noise) to reach the underlying analytic solution or data.

Static Public Attributes
static constexpr Options::String	help
static constexpr size_t	volume_dim = 3

Friends
bool	operator== (const PureSphericalHarmonic &lhs, const PureSphericalHarmonic &rhs)
bool	operator!= (const PureSphericalHarmonic &lhs, const PureSphericalHarmonic &rhs)

Detailed Description

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

Details

The initial data is taken from [188] , 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) = e^{- (r - r_0)^2 / w^2} Y_{lm}(\theta, \phi), \end{align}

where \(r_0\) is the radius of the profile 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 different background spacetimes.

Member Typedef Documentation

◆ tags

using CurvedScalarWave::AnalyticData::PureSphericalHarmonic::tags

Initial value:

 
      tmpl::list<CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi,
                 CurvedScalarWave::Tags::Phi<3>>

Member Function Documentation

◆ get_clone()

auto CurvedScalarWave::AnalyticData::PureSphericalHarmonic::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

◆ help

Options::String CurvedScalarWave::AnalyticData::PureSphericalHarmonic::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."}

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

src/PointwiseFunctions/AnalyticData/CurvedWaveEquation/PureSphericalHarmonic.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends