Cce::InnerBoundaryWeyl Struct Reference

Compute the Weyl scalar ${\mathrm{\Psi }}_0$ and its radial derivative ${\partial }_{\lambda }{\mathrm{\Psi }}_0$ on the inner boundary of CCE domain. The quantities are in the Cauchy coordinates. More...

#include <NewmanPenrose.hpp>

Public Types
using	return_tags = implementation defined
using	argument_tags = implementation defined

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)

Detailed Description

Compute the Weyl scalar ${\mathrm{\Psi }}_0$ and its radial derivative ${\partial }_{\lambda }{\mathrm{\Psi }}_0$ on the inner boundary of CCE domain. The quantities are in the Cauchy coordinates.

Details

The radial derivative of the Weyl scalar ${\partial }_{\lambda }{\mathrm{\Psi }}_0$ is given by

$$\begin{array}{r}{\partial }_{\lambda }{\mathrm{\Psi }}_0=\frac{(1-y{)}^2}{2r}{e}^{-2\beta }{\partial }_y{\mathrm{\Psi }}_0\end{array}$$

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

$$\begin{array}{rlr}& r=\omega \hat{r}& \beta =\hat{\beta }-\frac{1}{2}\log \omega \end{array}$$

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

• src/Evolution/Systems/Cce/NewmanPenrose.hpp