SpECTRE  v2021.11.01
Ccz4::Tags Namespace Reference

Tags for the CCZ4 formulation of Einstein equations. More...

Classes

struct  ATilde
 The trace-free part of the extrinsic curvature. More...
 
struct  ChristoffelSecondKind
 The spatial christoffel symbols of the second kind. More...
 
struct  ConformalChristoffelSecondKind
 The conformal spatial christoffel symbols of the second kind. More...
 
struct  ConformalFactor
 The conformal factor that rescales the spatial metric. More...
 
struct  ConformalFactorSquared
 The square of the conformal factor that rescales the spatial metric. More...
 
struct  ContractedConformalChristoffelSecondKind
 The contraction of the conformal spatial Christoffel symbols of the second kind. More...
 
struct  DerivConformalChristoffelSecondKind
 The spatial derivative of the conformal spatial christoffel symbols of the second kind. More...
 
struct  DerivContractedConformalChristoffelSecondKind
 The spatial derivative of the contraction of the conformal spatial Christoffel symbols of the second kind. More...
 
struct  DivergenceLapse
 The divergence of the lapse. More...
 
struct  FieldA
 Auxiliary variable which is analytically the spatial derivative of the natural log of the lapse. More...
 
struct  FieldB
 Auxiliary variable which is analytically the spatial derivative of the shift. More...
 
struct  FieldD
 Auxiliary variable which is analytically half the spatial derivative of the conformal spatial metric. More...
 
struct  FieldDUp
 Identity which is analytically negative one half the spatial derivative of the inverse conformal spatial metric. More...
 
struct  FieldP
 Auxiliary variable which is analytically the spatial derivative of the natural log of the conformal factor. More...
 
struct  GammaHat
 The CCZ4 evolved variable \(\hat{\Gamma}^i\). More...
 
struct  GammaHatMinusContractedConformalChristoffel
 The CCZ4 temporary expression \(\hat{\Gamma}^i - \tilde{\Gamma}^i\). More...
 
struct  GradGradLapse
 The gradient of the gradient of the lapse. More...
 
struct  GradSpatialZ4Constraint
 The gradient of the spatial part of the Z4 constraint. More...
 
struct  LogConformalFactor
 The natural log of the conformal factor. More...
 
struct  LogLapse
 The natural log of the lapse. More...
 
struct  Ricci
 The spatial Ricci tensor. More...
 
struct  RicciScalarPlusDivergenceZ4Constraint
 The sum of the Ricci scalar and twice the divergence of the upper spatial Z4 constraint. More...
 
struct  SpatialZ4Constraint
 The spatial part of the Z4 constraint. More...
 
struct  SpatialZ4ConstraintUp
 The spatial part of the upper Z4 constraint. More...
 
struct  TraceATilde
 The trace of the trace-free part of the extrinsic curvature. More...
 

Typedefs

template<size_t Dim, typename Frame , typename DataType >
using ConformalMetric = gr::Tags::Conformal< gr::Tags::SpatialMetric< Dim, Frame, DataType >, 2 >
 The conformally scaled spatial metric. More...
 
template<size_t Dim, typename Frame , typename DataType >
using InverseConformalMetric = gr::Tags::Conformal< gr::Tags::InverseSpatialMetric< Dim, Frame, DataType >, -2 >
 The conformally scaled inverse spatial metric. More...
 

Detailed Description

Tags for the CCZ4 formulation of Einstein equations.

Typedef Documentation

◆ ConformalMetric

template<size_t Dim, typename Frame , typename DataType >
using Ccz4::Tags::ConformalMetric = typedef gr::Tags::Conformal<gr::Tags::SpatialMetric<Dim, Frame, DataType>, 2>

The conformally scaled spatial metric.

Details

If \(\phi\) is the conformal factor and \(\gamma_{ij}\) is the spatial metric, then we define \(\bar{\gamma}_{ij} = \phi^2 \gamma_{ij}\).

◆ InverseConformalMetric

template<size_t Dim, typename Frame , typename DataType >
using Ccz4::Tags::InverseConformalMetric = typedef gr::Tags::Conformal<gr::Tags::InverseSpatialMetric<Dim, Frame, DataType>, -2>

The conformally scaled inverse spatial metric.

Details

If \(\phi\) is the conformal factor and \(\gamma^{ij}\) is the inverse spatial metric, then we define \(\bar{\gamma}^{ij} = \phi^{-2} \gamma^{ij}\).