SpECTRE  v2024.03.19
Cce::VolumeWeyl< Tags::Psi0Match > Struct Reference

Compute the Weyl scalar \(\Psi_0\) in the volume for the purpose of CCM, the quantity is in the Cauchy coordinates. More...

#include <NewmanPenrose.hpp>

Public Types

using return_tags = tmpl::list< Tags::Psi0Match >
 
using argument_tags = tmpl::list< Tags::BondiJCauchyView, Tags::Dy< Tags::BondiJCauchyView >, Tags::Dy< Tags::Dy< Tags::BondiJCauchyView > >, Tags::BoundaryValue< Tags::BondiR >, Tags::OneMinusY, Tags::LMax >
 

Static Public Member Functions

static void apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 2 > > * > psi_0, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &bondi_j_cauchy, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_j_cauchy, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_dy_j_cauchy, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &bondi_r_cauchy, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &one_minus_y, const size_t l_max)
 

Detailed Description

Compute the Weyl scalar \(\Psi_0\) in the volume for the purpose of CCM, the quantity is in the Cauchy coordinates.

Details

The Weyl scalar \(\Psi_0\) is given by:

\begin{align*} \Psi_0 = \frac{(1 - y)^4}{16 r^2 K} \bigg[& \partial_y \beta \left((1 + K) (\partial_y J) - \frac{J^2 \partial_y \bar J}{1 + K}\right) - \frac{1}{2} (1 + K) (\partial_y^2 J) + \frac{J^2 \partial_y^2 \bar J}{2(K + 1)}\\ & + \frac{1}{K^2} \left(- \frac{1}{4} J \left(\bar{J}^2 \left(\partial_y J\right)^2 + J^2 \left(\partial_y \bar J\right)^2\right) + \frac{1 + K^2}{2} J (\partial_y J) (\partial_y \bar J) \right)\bigg]. \end{align*}

The quantities above are all in the Cauchy coordinates, where \(K\) is updated from \(J\) and \(\bar J\), \((1-y)\) is invariant under the coordinate transformation. \(r\) transforms as

\begin{align*} r = \omega \hat r \end{align*}


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