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SpECTRE
v2024.04.12
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Apply a radius-independent angular gauge transformation to a volume \(J\), for use with initial data generation. More...
#include <InitializeJ.hpp>
Public Types | |
| using | boundary_tags = tmpl::list< Tags::PartiallyFlatGaugeC, Tags::PartiallyFlatGaugeD, Tags::PartiallyFlatGaugeOmega, Tags::CauchyAngularCoords, Spectral::Swsh::Tags::LMax > |
| using | return_tags = tmpl::list< Tags::BondiJ > |
| using | argument_tags = tmpl::append< boundary_tags > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > volume_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &gauge_c, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &gauge_d, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &gauge_omega, const tnsr::i< DataVector, 2, ::Frame::Spherical<::Frame::Inertial > > &cauchy_angular_coordinates, const Spectral::Swsh::SwshInterpolator &interpolator, size_t l_max) |
Apply a radius-independent angular gauge transformation to a volume \(J\), for use with initial data generation.
Performs the gauge transformation to \(\hat J\),
\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 \(K = \sqrt{1 + J \bar J}\).