SpECTRE  v2021.12.06
Cce::CalculateScriPlusValue< Tags::ScriPlus< Tags::Psi1 > > Struct Reference

Computes the leading part of \(\Psi_1\) near \(\mathcal I^+\). More...

#include <ScriPlusValues.hpp>

Public Types

using return_tags = tmpl::list< Tags::ScriPlus< Tags::Psi1 > >
 
using tensor_argument_tags = tmpl::list< Tags::Dy< Tags::Dy< Tags::BondiBeta > >, Spectral::Swsh::Tags::Derivative< Tags::Dy< Tags::Dy< Tags::BondiBeta > >, Spectral::Swsh::Tags::Eth >, Tags::Dy< Tags::BondiJ >, Tags::Dy< Tags::BondiQ >, Tags::Dy< Tags::Dy< Tags::BondiQ > >, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR >, Tags::EthRDividedByR >
 
using argument_tags = tmpl::push_back< tensor_argument_tags, Tags::LMax, Tags::NumberOfRadialPoints >
 

Static Public Member Functions

static void apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 1 > > * > psi_1, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &dy_dy_bondi_beta, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &eth_dy_dy_bondi_beta, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_bondi_j, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &dy_bondi_q, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &dy_dy_bondi_q, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &boundary_r, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &eth_r_divided_by_r, size_t l_max, size_t number_of_radial_points)
 

Detailed Description

Computes the leading part of \(\Psi_1\) near \(\mathcal I^+\).

Details

The value \(\Psi_1\) scales asymptotically as \(r^{-4}\), and has the form (in the coordinates used for regularity preserving CCE)

\begin{align*} \Psi_1^{(4)} = \frac{1}{8} \left(- 12 \eth \beta^{(2)} + J^{(1)} \bar Q^{(1)} + 2 Q^{(2)}\right) \end{align*}

where \(A^{(n)}\) is the \(1/r^n\) part of \(A\) evaluated at \(\mathcal I^+\), so for any quantity \(A\),

\begin{align*} \eth A^{(2)} &= (2 R^2 \eth \partial_y^2 A + 2 R \eth R \partial^2_y A)|_{y = 1}, \notag\\ A^{(1)} &= (- 2 R \partial_y A)|_{y = 1}, \notag\\ A^{(2)} &= (2 R^2 \partial_y^2 A)|_{y = 1}, \end{align*}

where the expansion is determined by the conversion between Bondi and numerical radii \(r = 2 R / (1 - y)\).


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