SpECTRE  v2021.12.06
Cce::GaugeAdjustedBoundaryValue< Tags::BondiQ > Struct Reference

Computes the evolution gauge quantity \(\hat Q\) on the worldtube. More...

#include <GaugeTransformBoundaryData.hpp>

Public Types

using return_tags = tmpl::list< Tags::EvolutionGaugeBoundaryValue< Tags::BondiQ > >
 
using argument_tags = tmpl::list< Tags::BoundaryValue< Tags::Dr< Tags::BondiU > >, Tags::BondiJ, Tags::Dy< Tags::BondiJ >, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR >, Tags::EvolutionGaugeBoundaryValue< Tags::BondiBeta >, Tags::PartiallyFlatGaugeC, Tags::PartiallyFlatGaugeD, 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, 1 > > * > evolution_gauge_q, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &cauchy_gauge_dr_u, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &volume_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &volume_dy_j, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &evolution_gauge_r, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &evolution_gauge_beta, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &gauge_c, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &gauge_d, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &omega, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &eth_omega, const Spectral::Swsh::SwshInterpolator &interpolator, const size_t l_max)
 

Detailed Description

Computes the evolution gauge quantity \(\hat Q\) on the worldtube.

Details

The evolution gauge quantity \(\hat Q\) obeys

\begin{align*} \hat Q =& \hat r^2 e^{-2 \hat \beta} (\hat K \partial_{\hat r} \hat U + \hat J \partial_{\hat r} \hat{\bar U}),\\ \partial_{\hat r} \hat U =& \frac{1}{2 \hat \omega^3}\left(\hat{\bar d} \partial_r U(\hat x^{\hat A}) - \hat c \partial_r \bar U(\hat x^{\hat A})\right) + \frac{e^{2\hat \beta}}{\hat r^2 \hat \omega} \left(\hat J \hat{\bar{\eth}} \hat \omega - \hat K \hat \eth \hat \omega\right) \left(-1 + \partial_{\hat y} \hat{\bar{J}} \partial_{\hat y} \hat J - \left[\frac{\partial_{\hat y}(\hat J \hat{\bar{J}})} {2 \hat K}\right]^2\right) \notag \\ & + 2 \frac{e^{2 \hat \beta}}{\hat \omega \hat r^2} \left[ \hat{\bar{\eth}} \hat \omega \partial_{\hat y} \hat J + \hat{\eth} \hat \omega \left(-\frac{\hat J \partial_{\hat y} \hat{\bar J} + \hat{\bar J} \partial_{\hat y} \hat J}{2 \hat K}\right) \right]. \end{align*}

where the explicit argument \(\hat x^{\hat A}\) on the right-hand side implies the need for an interpolation operation, and \(K = \sqrt{1 + J \bar J}\).


The documentation for this struct was generated from the following file: