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SpECTRE
v2024.04.12
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Computes the evolution gauge quantity \(\hat H\) on the worldtube. More...
#include <GaugeTransformBoundaryData.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::EvolutionGaugeBoundaryValue< Tags::BondiH > > |
| using | argument_tags = tmpl::list< Tags::BondiJ, Tags::BoundaryValue< Tags::Du< Tags::BondiJ > >, Tags::Dy< Tags::BondiJ >, Tags::BondiUAtScri, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR >, Tags::PartiallyFlatGaugeC, Tags::PartiallyFlatGaugeD, Tags::PartiallyFlatGaugeOmega, Tags::Du< Tags::PartiallyFlatGaugeOmega >, Spectral::Swsh::Tags::Derivative< Tags::PartiallyFlatGaugeOmega, Spectral::Swsh::Tags::Eth >, Tags::EvolutionGaugeBoundaryValue< Tags::DuRDividedByR >, Spectral::Swsh::Tags::SwshInterpolator< Tags::CauchyAngularCoords >, Tags::LMax > |
Static Public Member Functions | |
| static void | apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > evolution_gauge_h, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &volume_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &cauchy_gauge_du_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &volume_dy_j, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &evolution_gauge_u_at_scri, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &evolution_gauge_r, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &gauge_c, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &gauge_d, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &omega, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &du_omega, const Scalar< SpinWeighted< ComplexDataVector, 1 > > ð_omega, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &evolution_gauge_du_r_divided_by_r, const Spectral::Swsh::SwshInterpolator &interpolator, const size_t l_max) |
Computes the evolution gauge quantity \(\hat H\) on the worldtube.
The evolution gauge \(\hat H\) obeys
\begin{align*} \hat H =& \frac{1}{2} \left(\mathcal{U}^{(0)} \hat{\bar \eth} \hat J + \bar{\mathcal{U}}^{(0)} \hat{\eth} \hat J\right) + \frac{\partial_{\hat u} \hat \omega - \tfrac{1}{2} \left(\mathcal{U}^{(0)} \bar{\hat \eth}\hat \omega + \bar{\mathcal{U}}^{(0)} \hat \eth \hat \omega \right) }{\hat \omega} \left(2 \hat J - 2 \partial_{\hat y} \hat J\right) - \hat J\hat{\bar \eth} \mathcal{U}^{(0)} + \hat K \hat \eth \bar{\mathcal{U}}^{(0)} \notag\\ &+ \frac{1}{4 \hat \omega^2} \left(\hat{\bar d}^2 H(\hat x^{\hat A}) + \hat c^2 \bar H(\hat x^{\hat A}) + \hat{\bar d} \hat c \frac{H(\hat x^{\hat A}) \bar J(\hat x^{\hat A}) + J(\hat x^{\hat A}) \bar H(\hat x^{\hat A})}{K}\right) + 2 \frac{\partial_u R}{R} \partial_{\hat y} J \end{align*}
where the superscript \((0)\) denotes evaluation at \(\mathcal I^+\) and the explicit \(\hat x^{\hat A}\) arguments on the right-hand side imply interpolation operations, and \(K = \sqrt{1 + J \bar J}\), \(\hat K = \sqrt{1 + \hat J \hat{\bar J}}\).