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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 = implementation defined
 
using tags = implementation defined
 

Public Member Functions

 PureSphericalHarmonic (double radius, double width, std::pair< size_t, int > mode, const Options::Context &context={})
 
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 &)
 

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 [172] , Eqs. 4.1–4.3, and sets the evolved variables of the scalar wave as follows:

(1)Ψ=0(2)Φi=0(3)Π=Π0(r,θ,ϕ)=e(rr0)2/w2Ylm(θ,ϕ),

where r0 is the radius of the profile and w is its width. This describes a pure spherical harmonic mode Ylm(θ,ϕ) truncated by a circular Gaussian window function.

When evolved, the scalar field Φ will briefly build up around the radius r0 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: