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SpECTRE
v2024.04.12
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Compute the Weyl scalar \(\Psi_0\) and its radial derivative \(\partial_\lambda \Psi_0\) on the inner boundary of CCE domain. The quantities are in the Cauchy coordinates. More...
#include <NewmanPenrose.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::BoundaryValue< Tags::Psi0Match >, Tags::BoundaryValue< Tags::Dlambda< Tags::Psi0Match > > > |
| using | argument_tags = tmpl::list< Tags::Psi0Match, Tags::Dy< Tags::Psi0Match >, Tags::OneMinusY, Tags::BoundaryValue< Tags::BondiR >, Tags::BoundaryValue< Tags::BondiBeta >, Tags::LMax > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > psi_0_boundary, gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > dlambda_psi_0_boundary, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &psi_0, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_psi_0, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &one_minus_y, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &bondi_r_cauchy, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &bondi_beta_cauchy, const size_t l_max) |
Compute the Weyl scalar \(\Psi_0\) and its radial derivative \(\partial_\lambda \Psi_0\) on the inner boundary of CCE domain. The quantities are in the Cauchy coordinates.
The radial derivative of the Weyl scalar \(\partial_\lambda \Psi_0\) is given by
\begin{align*} \partial_\lambda \Psi_0 = \frac{(1-y)^2}{2r}e^{-2\beta} \partial_y \Psi_0 \end{align*}
Note that \((1-y)\), \(r\), and \(\beta\) are in the Cauchy coordinates, where \((1-y)\) is invariant under the coordinate transformation, while \(r\) and \(\beta\) transform as
\begin{align*} &r = \omega \hat r & \beta = \hat \beta - \frac{1}{2} \log \omega \end{align*}