Compute the contribution to the leading \(\Psi_4\) that corresponds to a total time derivative. More...

#include <ScriPlusValues.hpp>

Public Types
using	return_tags = tmpl::list< Tags::TimeIntegral< Tags::ScriPlus< Tags::Psi4 > > >

using	tensor_argument_tags = tmpl::list< Tags::Exp2Beta, Tags::Dy< Tags::BondiU >, Spectral::Swsh::Tags::Derivative< Tags::Dy< Tags::BondiU >, Spectral::Swsh::Tags::Eth >, Tags::Dy< Tags::Du< Tags::BondiJ > >, Tags::EvolutionGaugeBoundaryValue< Tags::BondiR >, Tags::EthRDividedByR >

using	argument_tags = tmpl::append< tensor_argument_tags, tmpl::list< Tags::LMax, Tags::NumberOfRadialPoints > >

Static Public Member Functions
static void	apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, -2 > > * > integral_of_psi_4, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &exp_2_beta, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &dy_bondi_u, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &eth_dy_bondi_u, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &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

Compute the contribution to the leading \(\Psi_4\) that corresponds to a total time derivative.

The value \(\Psi_4\) scales asymptotically as \(r^{-1}\), and has the form

\begin{align*} \Psi_4^{(1)} = \partial_{u_{\text{inertial}}} B, \end{align*}

where superscripts denote orders in the expansion in powers of \(r^{-1}\). This mutator computes \(B\):

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

and the time derivative that appears the original equation obeys,

\[ \partial_{u_{\text{inertial}}} = e^{-2 \beta} \partial_u \]

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

Public Types