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SpECTRE
v2024.08.03
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From the angular coordinates AngularCoordinateTag and the Cartesian coordinates CartesianCoordinateTag, determine the spin-weighted Jacobian factors GaugeFactorSpin2 and GaugeFactorSpin0.
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#include <GaugeTransformBoundaryData.hpp>
Public Types | |
| using | return_tags = tmpl::list< GaugeFactorSpin2, GaugeFactorSpin0, AngularCoordinateTag > |
| using | argument_tags = tmpl::list< CartesianCoordinateTag, Tags::LMax > |
Static Public Member Functions | |
| static void | apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > gauge_factor_spin_2, const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 0 > > * > gauge_factor_spin_0, const gsl::not_null< tnsr::i< DataVector, 2, ::Frame::Spherical<::Frame::Inertial > > * > angular_source_coordinates, const tnsr::i< DataVector, 3 > &cartesian_source_coordinates, const size_t l_max) |
From the angular coordinates AngularCoordinateTag and the Cartesian coordinates CartesianCoordinateTag, determine the spin-weighted Jacobian factors GaugeFactorSpin2 and GaugeFactorSpin0.
This is most often used in the context of generating the Jacobians in the evolution-gauge coordinates from the Cauchy collocation points as a function of the evolution gauge coordinates. In this concrete case, the GaugeFactorSpin2 is the gauge factor \(\hat c\) and takes the value
\begin{align*} \hat c = \hat q^{\hat A} \partial_{\hat A}(x^A) q_A, \end{align*}
and the GaugeFactorSpin0 is the gauge factor \(\hat d\) and takes the value
\begin{align*} \hat d = \hat{\bar q}^{\hat A} \partial_{\hat A}(x^A) q_A. \end{align*}
The more generic template construction is employed so that the spin-weighted Jacobians can also be computed between two arbitrary gauges, including the inverse Jacobians associated with moving from the evolution gauge to the Cauchy gauge.