Analytic solution representing a coordinate oscillation about a stationary Schwarzschild black hole.
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| WRAPPED_PUPable_decl_template (BouncingBlackHole) |
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| BouncingBlackHole (CkMigrateMessage *msg) |
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| BouncingBlackHole (double amplitude, double extraction_radius, double mass, double period) |
| std::unique_ptr< WorldtubeData > | get_clone () const override |
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void | pup (PUP::er &p) override |
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| WRAPPED_PUPable_abstract (WorldtubeData) |
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| WorldtubeData (const double extraction_radius) |
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| WorldtubeData (CkMigrateMessage *msg) |
| template<typename... Tags> |
| tuples::TaggedTuple< Tags... > | variables (const size_t output_l_max, const double time, tmpl::list< Tags... >) const |
| | Retrieve worldtube data represented by the analytic solution, at boundary angular resolution l_max and time time
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void | pup (PUP::er &p) override |
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virtual std::unique_ptr< Cce::InitializeJ::InitializeJ< false > > | get_initialize_j (const double) const |
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virtual bool | use_noninertial_news () const |
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| void | prepare_solution (const size_t, const double) const override |
| void | variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > spacetime_metric, size_t l_max, double time, tmpl::type_< gr::Tags::SpacetimeMetric< DataVector, 3 > >) const override |
| | The implementation function that computes the spacetime metric on the extraction sphere at collocation points associated with angular resolution l_max.
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| void | variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > dt_spacetime_metric, size_t l_max, double time, tmpl::type_< ::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >) const override |
| | The implementation function that computes the first time derivative of the spacetime metric on the extraction sphere.
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| void | variables_impl (gsl::not_null< tnsr::iaa< DataVector, 3 > * > d_spacetime_metric, size_t l_max, double time, tmpl::type_< gh::Tags::Phi< DataVector, 3 > >) const override |
| | The implementation function that computes the first spatial derivative of the spacetime metric on the extraction sphere.
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| void | variables_impl (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 > > * > news, size_t output_l_max, double time, tmpl::type_< Tags::News >) const override |
| | The News in the bouncing black hole solution vanishes, as the oscillation comes entirely from a coordinate transform.
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| virtual void | variables_impl (gsl::not_null< tnsr::i< DataVector, 3 > * > cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::CauchyCartesianCoords >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::i< DataVector, 3 > * > dr_cartesian_coordinates, size_t output_l_max, double time, tmpl::type_< Tags::Dr< Tags::CauchyCartesianCoords > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > dt_spacetime_metric, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::SpacetimeMetric< DataVector, 3 > > >) const=0 |
| virtual void | variables_impl (gsl::not_null< tnsr::aa< DataVector, 3 > * > pi, size_t output_l_max, double time, tmpl::type_< gh::Tags::Pi< DataVector, 3 > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > spatial_metric, size_t output_l_max, double time, tmpl::type_< gr::Tags::SpatialMetric< DataVector, 3 > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > dt_spatial_metric, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::SpatialMetric< DataVector, 3 > > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::ii< DataVector, 3 > * > dr_spatial_metric, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::SpatialMetric< DataVector, 3 > > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > shift, size_t output_l_max, double time, tmpl::type_< gr::Tags::Shift< DataVector, 3 > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > dt_shift, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::Shift< DataVector, 3 > > >) const |
| virtual void | variables_impl (gsl::not_null< tnsr::I< DataVector, 3 > * > dr_shift, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::Shift< DataVector, 3 > > >) const |
| virtual void | variables_impl (gsl::not_null< Scalar< DataVector > * > lapse, size_t output_l_max, double time, tmpl::type_< gr::Tags::Lapse< DataVector > >) const |
| virtual void | variables_impl (gsl::not_null< Scalar< DataVector > * > dt_lapse, size_t output_l_max, double time, tmpl::type_<::Tags::dt< gr::Tags::Lapse< DataVector > > >) const |
| virtual void | variables_impl (gsl::not_null< Scalar< DataVector > * > dr_lapse, size_t output_l_max, double time, tmpl::type_< Tags::Dr< gr::Tags::Lapse< DataVector > > >) const |
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template<typename Tag> |
| const auto & | cache_or_compute (const size_t output_l_max, const double time) const |
Analytic solution representing a coordinate oscillation about a stationary Schwarzschild black hole.
Details
As the oscillation in the metric data at the worldtube is a pure coordinate effect, the system evolved using this worldtube data should produce zero news. The solution is a coordinate transform applied to the Schwarzschild solution in Kerr-Schild coordinates.
The implementation function that computes the first time derivative of the spacetime metric on the extraction sphere.
Details
The time derivative of the spacetime metric \(\partial_t g_{a b}\) comes entirely from the Jacobian factor:
\begin{align*}\partial_t x = \frac{8 \pi A}{T} \cos\left(\frac{2 \pi t}{T}\right)
\left(\sin\left(\frac{2 \pi t}{T}\right)\right)^3,
\end{align*}
so the transformed metric derivative is,
\begin{align*}\partial_t g_{a^\prime b^\prime} = 2 \partial_{(a^\prime} \partial_t x
\partial_{b^\prime)} x^a g_{x a}.
\end{align*}
In this notation we take the primed coordinates to be the coordinates for which the black hole has time-dependent coordinate position.
The implementation function that computes the spacetime metric on the extraction sphere at collocation points associated with angular resolution l_max.
Details
The spacetime metric \(g_{a b}\) is determined by evaluating the Kerr-Schild metric at a set of transformed coordinates \(t^\prime = t,
y^\prime = y, z^\prime = z\), and
\begin{align*}x = x^\prime + A \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^4,
\end{align*}
where the amplitude \(A\) is set by the option Amplitude and the period \(T\) is set by the option Period. In this notation we take the primed coordinates to be the coordinates for which the black hole has time-dependent coordinate position.
Implements Cce::Solutions::WorldtubeData.
The implementation function that computes the first spatial derivative of the spacetime metric on the extraction sphere.
Details
The calculation proceeds by standard coordinate transform techniques for the transformation given by \(t^\prime = t,
y^\prime = y, z^\prime = z\), and
\begin{align*}x = x^\prime + A \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^4,
\end{align*}
The general coordinate transformation formula that gives the metric is then
\begin{align*}\partial_a g_{b c} =
\partial_a \partial_b x^{\prime a^\prime} \partial_c x^{\prime b^\prime}
g_{a^\prime b^\prime}
+ \partial_b x^{\prime a^\prime} \partial_a \partial_c x^{\prime b^\prime}
g_{a^\prime b^\prime}
+ \partial_a x^{\prime a^\prime} \partial_b x^{\prime b^\prime}
\partial_c x^{\prime c^\prime} \partial_a g_{b c}
\end{align*}
Implements Cce::Solutions::WorldtubeData.