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
using	argument_tags

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 \(\Psi_0\) and its radial derivative \(\partial_\lambda \Psi_0\) on the inner boundary of CCE domain. The quantities are in the Cauchy coordinates.

Details

The radial derivative of the Weyl scalar \(\partial_\lambda \Psi_0\) 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*}

Member Typedef Documentation

◆ argument_tags

using Cce::InnerBoundaryWeyl::argument_tags

Initial value:

 
      tmpl::list<Tags::Psi0Match, Tags::Dy<Tags::Psi0Match>, Tags::OneMinusY,
                 Tags::BoundaryValue<Tags::BondiR>,
                 Tags::BoundaryValue<Tags::BondiBeta>, Tags::LMax>

◆ return_tags

using Cce::InnerBoundaryWeyl::return_tags