Computes the leading part of \(\Psi_0\) near \(\mathcal I^+\). More...

#include <ScriPlusValues.hpp>

Public Types
using	return_tags = tmpl::list< Tags::ScriPlus< Tags::Psi0 > >

using	tensor_argument_tags = tmpl::list< Tags::Dy< Tags::BondiJ >, Tags::Dy< Tags::Dy< Tags::Dy< Tags::BondiJ > > >, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR > >

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, 2 > > * > psi_0, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_bondi_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_dy_dy_bondi_j, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &boundary_r, size_t l_max, size_t number_of_radial_points)

Detailed Description

Computes the leading part of \(\Psi_0\) near \(\mathcal I^+\).

The value \(\Psi_0\) scales asymptotically as \(r^{-5}\), and has the form (in the coordinates used for regularity preserving CCE)

\begin{align*} \Psi_0^{(5)} = \frac{3}{2}\left(\frac{1}{4}\bar J^{(1)} J^{(1)} {}^2 - J^{(3)}\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*} A^{(1)} &= (- 2 R \partial_y A)|_{y = 1} \notag\\ A^{(3)} &= \left(-\frac{4}{3} R^3 \partial_y^3 A\right)|_{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:

Public Types