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

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

virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

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 [182] , 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 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

constexpr 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