SpECTRE  v2023.05.16
CurvedScalarWave::Worldtube::TimeDerivativeMutator Struct Reference

Calculates the time derivative of Psi0, the constant coefficient of the expansion of Psi. More...

#include <TimeDerivative.hpp>

Public Types

using variables_tag = ::Tags::Variables< tmpl::list< Tags::Psi0, Tags::dtPsi0 > >
using dt_variables_tag = db::add_tag_prefix<::Tags::dt, variables_tag >
using return_tags = tmpl::list< dt_variables_tag >
using argument_tags = tmpl::list< variables_tag, Stf::Tags::StfTensor< Tags::PsiWorldtube, 0, Dim, Frame::Grid >, Stf::Tags::StfTensor< Tags::PsiWorldtube, 1, Dim, Frame::Grid >, Stf::Tags::StfTensor< Tags::PsiWorldtube, 2, Dim, Frame::Grid >, Stf::Tags::StfTensor<::Tags::dt< Tags::PsiWorldtube >, 1, Dim, Frame::Grid >, gr::Tags::InverseSpacetimeMetric< double, Dim, Frame::Grid >, gr::Tags::TraceSpacetimeChristoffelSecondKind< double, Dim, Frame::Grid >, Tags::ExcisionSphere< Dim > >

Static Public Member Functions

static void apply (const gsl::not_null< Variables< tmpl::list<::Tags::dt< Tags::Psi0 >, ::Tags::dt< Tags::dtPsi0 > > > * > dt_evolved_vars, const Variables< tmpl::list< Tags::Psi0, Tags::dtPsi0 > > &evolved_vars, const Scalar< double > &psi_monopole, const tnsr::i< double, Dim, Frame::Grid > &psi_dipole, const tnsr::ii< double, Dim, Frame::Grid > &psi_quadrupole, const tnsr::i< double, Dim, Frame::Grid > &dt_psi_dipole, const tnsr::AA< double, Dim, Frame::Grid > &inverse_spacetime_metric, const tnsr::A< double, Dim, Frame::Grid > &trace_spacetime_christoffel, const ExcisionSphere< Dim > &excision_sphere)

Static Public Attributes

static constexpr size_t Dim = 3

Detailed Description

Calculates the time derivative of Psi0, the constant coefficient of the expansion of Psi.


The derivation comes from expanding the scalar wave equation to second order and reads

\begin{equation} g^{00}_0 \ddot{\Psi}^R_0(t_s) + 2 g_0^{0i} \dot{\Psi}^N_i(t_s) + 2 g_0^{ij} \Psi^N_{\langle ij \rangle}(t_s) + \frac{2 \delta_{ij} g_0^{ij}}{R^2} \left(\Psi^N_0(t_s) - \Psi^R_0(t_s) \right) - \Gamma_0^0\dot{\Psi}R_0(t_s) - \Gamma_0^i \Psi_i^N(t_s) = 0. *\end{equation}

Here, \( \Gamma^\mu_0 \) and \( g^{\mu \nu}_0 \) are the trace of the spacetime Christoffel symbol and the inverse spacetime metric, respectively, evaluated at the position of the particle; \(\Psi^N_0\), \(\Psi^N_i\), \(\Psi^N_\langle i j \rangle\) are the monopole, dipole and quadrupole of the regular field on the worldtube boundary transformed to symmetric trace-free tensors and \( R\) is the worldtube radius.

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