SpECTRE  v2021.12.06
CurvedScalarWave::AnalyticData::PureSphericalHarmonic Class Reference

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 >
 

Public Member Functions

 PureSphericalHarmonic (double radius, double width, std::pair< size_t, int > mode, const Options::Context &context={})
 
tuples::TaggedTuple< CurvedScalarWave::Pi, CurvedScalarWave::Phi< 3 >, CurvedScalarWave::Psivariables (const tnsr::I< DataVector, 3 > &x, double, tmpl::list< CurvedScalarWave::Pi, CurvedScalarWave::Phi< 3 >, CurvedScalarWave::Psi >) const
 Retrieve the evolution variables at spatial coordinates x
 
void pup (PUP::er &)
 

Static Public Attributes

static constexpr Options::String help
 

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 [100] , 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 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: