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SpECTRE
v2024.04.12
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Computes the evolution gauge quantity \(\hat W\) on the worldtube. More...
#include <GaugeTransformBoundaryData.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::EvolutionGaugeBoundaryValue< Tags::BondiW > > |
| using | argument_tags = tmpl::list< Tags::BoundaryValue< Tags::BondiW >, Tags::BondiJ, Tags::EvolutionGaugeBoundaryValue< Tags::BondiU >, Tags::EvolutionGaugeBoundaryValue< Tags::BondiBeta >, Tags::BondiUAtScri, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR >, Tags::PartiallyFlatGaugeOmega, Tags::Du< Tags::PartiallyFlatGaugeOmega >, Spectral::Swsh::Tags::Derivative< Tags::PartiallyFlatGaugeOmega, Spectral::Swsh::Tags::Eth >, Spectral::Swsh::Tags::SwshInterpolator< Tags::CauchyAngularCoords >, Tags::LMax > |
Static Public Member Functions | |
| static void | apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 0 > > * > evolution_gauge_w, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &cauchy_gauge_w, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &volume_j, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &evolution_gauge_u, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &evolution_gauge_beta, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &evolution_gauge_u_at_scri, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &evolution_gauge_r, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &omega, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &du_omega, const Scalar< SpinWeighted< ComplexDataVector, 1 > > ð_omega, const Spectral::Swsh::SwshInterpolator &interpolator, const size_t l_max) |
Computes the evolution gauge quantity \(\hat W\) on the worldtube.
The evolution gauge value \(\hat W\) obeys
\begin{align*} \hat W =& W(\hat x^{\hat A}) + (\hat \omega - 1) / \hat r + \frac{e^{2 \hat \beta}}{2 \hat \omega^2 \hat r} \left(\hat J \left(\hat{\bar \eth} \hat \omega\right)^2 + \hat{\bar{J}} \left(\hat \eth \hat \omega\right) ^2 - 2 K \left( \hat \eth \hat \omega\right) \left(\hat{\bar \eth} \hat \omega\right) \right) - \frac{2 \partial_{u} \hat \omega}{\hat \omega} - \frac{ \hat U \bar \eth \hat \omega + \hat{\bar U} \eth \hat \omega } {\hat \omega}, \end{align*}
where the explicit argument \(\hat x^{\hat A}\) on the right-hand side implies the need for an interpolation operation and \(K = \sqrt{1 + J \bar J}\).