Computes the leading part of \(\Psi_3\) near \(\mathcal I^+\). More...

#include <ScriPlusValues.hpp>

Public Types
using	return_tags = tmpl::list<Tags::ScriPlus<Tags::Psi3>>
using	tensor_argument_tags
using	argument_tags

Static Public Member Functions

static void apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -1 > > * > psi_3, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &exp_2_beta, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &eth_beta, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &eth_ethbar_beta, const Scalar< SpinWeighted< ComplexDataVector, -1 > > &ethbar_eth_ethbar_beta, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_du_bondi_j, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &ethbar_dy_du_bondi_j, 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 \(\Psi_3\) near \(\mathcal I^+\).

Details

The value \(\Psi_3\) scales asymptotically as \(r^{-2}\), and has the form (in the coordinates used for regularity preserving CCE)

\begin{align*}\Psi_3^{(2)} = 2 \bar \eth \beta^{(0)} + 4 \bar \eth \beta^{(0)} \eth \bar \eth \beta^{(0)} + \bar \eth \eth \bar \eth \beta^{(0)} + \frac{e^{-2 \beta^{(0)}}}{2} \eth \partial_u \bar J^{(1)} - e^{-2 \beta^{(0)}} \eth \beta^{(0)} \partial_u \bar J^{(1)} \end{align*}

,

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

\begin{align*}J^{(1)} = (-2 R \partial_y J)|_{y = 1}, \end{align*}

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

Member Typedef Documentation

◆ argument_tags

using Cce::CalculateScriPlusValue< Tags::ScriPlus< Tags::Psi3 > >::argument_tags

Initial value:

tmpl::push_back<tensor_argument_tags, Tags::LMax,

Tags::NumberOfRadialPoints>

◆ tensor_argument_tags

using Cce::CalculateScriPlusValue< Tags::ScriPlus< Tags::Psi3 > >::tensor_argument_tags