Analytic initial data for a pure spherical harmonic in three dimensions in a KerrSchild background.
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using | options = tmpl::list< Mass, Spin, Amplitude, Radius, Width, Mode > |
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template<typename DataType , typename Frame = Frame::Inertial> |
using | tags = tmpl::flatten< tmpl::list< typename AnalyticDataBase::template tags< DataType >, gr::Tags::DerivDetSpatialMetric< DataType, 3, Frame >, gr::Tags::TraceExtrinsicCurvature< DataType >, gr::Tags::SpatialChristoffelFirstKind< DataType, 3, Frame >, gr::Tags::SpatialChristoffelSecondKind< DataType, 3, Frame >, gr::Tags::TraceSpatialChristoffelSecondKind< DataType, 3, Frame > > > |
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template<typename DataType > |
using | tags = tmpl::push_back< typename gr::AnalyticDataBase< volume_dim >::template tags< DataType >, CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi, CurvedScalarWave::Tags::Phi< volume_dim > > |
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| KerrSphericalHarmonic (const KerrSphericalHarmonic &)=default |
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KerrSphericalHarmonic & | operator= (const KerrSphericalHarmonic &)=default |
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| KerrSphericalHarmonic (KerrSphericalHarmonic &&)=default |
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KerrSphericalHarmonic & | operator= (KerrSphericalHarmonic &&)=default |
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| KerrSphericalHarmonic (double mass, const std::array< double, 3 > &dimensionless_spin, double amplitude, double radius, double width, std::pair< size_t, int > mode) |
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auto | get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override |
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template<typename DataType , typename... Tags> |
tuples::TaggedTuple< Tags... > | variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tags... >) const |
| Retrieve a collection of scalar variables at x
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template<typename DataType , typename Tag > |
tuples::TaggedTuple< Tag > | variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag >) const |
| Retrieve the metric variables.
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void | pup (PUP::er &) override |
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template<typename DataType > |
auto | variables (const tnsr::I< DataType, 3 > &x, tmpl::list< CurvedScalarWave::Tags::Psi >) const -> tuples::TaggedTuple< CurvedScalarWave::Tags::Psi > |
| Retrieve scalar variable at x
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template<typename DataType > |
auto | variables (const tnsr::I< DataType, 3 > &x, tmpl::list< CurvedScalarWave::Tags::Phi< 3_st > >) const -> tuples::TaggedTuple< CurvedScalarWave::Tags::Phi< 3_st > > |
| Retrieve scalar variable at x
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template<typename DataType > |
auto | variables (const tnsr::I< DataType, 3 > &x, tmpl::list< CurvedScalarWave::Tags::Pi >) const -> tuples::TaggedTuple< CurvedScalarWave::Tags::Pi > |
| Retrieve scalar variable at x
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virtual auto | get_clone () const -> std::unique_ptr< InitialData >=0 |
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Analytic initial data for a pure spherical harmonic in three dimensions in a KerrSchild background.
Details
The initial data is taken from [162] , 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) = A e^{- (r - r_0)^2 / w^2} Y_{lm}(\theta, \phi), \end{align}
where \(A\) is the amplitude of the profile, \(r_0\) is its radius 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 the Kerr spacetime.
- See also
- CurvedScalarWave::AnalyticData::PureSphericalHarmonic and gr::Solutions::KerrSchild.