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SpECTRE
v2024.05.11
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Computes the evolution gauge \(\partial_{\hat u} \hat R / \hat R\) on the worldtube. More...
#include <GaugeTransformBoundaryData.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::EvolutionGaugeBoundaryValue< Tags::DuRDividedByR > > |
| using | argument_tags = tmpl::list< Tags::BoundaryValue< Tags::DuRDividedByR >, Tags::BondiUAtScri, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR >, Tags::PartiallyFlatGaugeOmega, Tags::Du< Tags::PartiallyFlatGaugeOmega >, Spectral::Swsh::Tags::SwshInterpolator< Tags::CauchyAngularCoords >, Tags::LMax > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 0 > > * > evolution_gauge_du_r_divided_by_r, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &cauchy_gauge_du_r_divided_by_r, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &bondi_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 Spectral::Swsh::SwshInterpolator &interpolator, size_t l_max) |
Computes the evolution gauge \(\partial_{\hat u} \hat R / \hat R\) on the worldtube.
The evolution gauge quantity \( \partial_{\hat u} \hat R / \hat R\) obeys
\begin{align*} \frac{\partial_{\hat u} \hat R}{ \hat R} = \frac{\partial_u R (\hat x^{\hat A})}{R(\hat x^{\hat A})} + \frac{\partial_{\hat u} \hat \omega}{\hat \omega} + \frac{\mathcal U^{(0)} \bar \eth R(\hat x^{\hat A}) + \bar{\mathcal U}^{(0)} \eth R(\hat x^{\hat A}) }{2 R(\hat x^{\hat A})} \end{align*}
note that the terms proportional to \(\eth R\) or its conjugate arise from the conversion between \(\partial_u\) and \(\partial_{\hat u}f\). The right-hand side quantities with explicit \(\hat x\) require interpolation. \(\mathcal U^{(0)}\) is the asymptotic quantity determined by GaugeUpdateTimeDerivatives.