SpECTRE  v2023.01.13
CurvedScalarWave::AnalyticData::PureSphericalHarmonic Class Reference

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

#include <PureSphericalHarmonic.hpp>

struct  Mode

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={})

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 [131] , 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.

## ◆ 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