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SpECTRE
v2024.09.29
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Computes the evolution gauge quantity \(\hat J\) on the worldtube. More...
#include <GaugeTransformBoundaryData.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::EvolutionGaugeBoundaryValue< Tags::BondiJ > > |
| using | argument_tags = tmpl::list< Tags::BoundaryValue< Tags::BondiJ >, Tags::PartiallyFlatGaugeC, Tags::PartiallyFlatGaugeD, Tags::PartiallyFlatGaugeOmega, Spectral::Swsh::Tags::SwshInterpolator< Tags::CauchyAngularCoords > > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > evolution_gauge_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &cauchy_gauge_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &gauge_c, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &gauge_d, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &omega, const Spectral::Swsh::SwshInterpolator &interpolator) |
Computes the evolution gauge quantity \(\hat J\) on the worldtube.
The evolution gauge quantity \(\hat J\) obeys
\begin{align*} \hat J = \frac{1}{4 \hat{\omega}^2} \left( \bar{\hat d}^2 J(\hat x^{\hat A}) + \hat c^2 \bar J(\hat x^{\hat A}) + 2 \hat c \bar{\hat d} K(\hat x^{\hat A}) \right) \end{align*}
Where \(\hat c\) and \(\hat d\) are the spin-weighted angular Jacobian factors computed by GaugeUpdateJacobianFromCoords, and \(\hat \omega\) is the conformal factor associated with the angular coordinate transformation. Note that the right-hand sides with explicit \(\hat x^{\hat A}\) dependence must be interpolated and that \(K = \sqrt{1 + J \bar J}\).