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SpECTRE
v2021.11.01
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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... | |
Tags for the CCZ4 formulation of Einstein equations.
| using Ccz4::Tags::ConformalMetric = typedef gr::Tags::Conformal<gr::Tags::SpatialMetric<Dim, Frame, DataType>, 2> |
The conformally scaled spatial metric.
If \(\phi\) is the conformal factor and \(\gamma_{ij}\) is the spatial metric, then we define \(\bar{\gamma}_{ij} = \phi^2 \gamma_{ij}\).
| using Ccz4::Tags::InverseConformalMetric = typedef gr::Tags::Conformal<gr::Tags::InverseSpatialMetric<Dim, Frame, DataType>, -2> |
The conformally scaled inverse spatial metric.
If \(\phi\) is the conformal factor and \(\gamma^{ij}\) is the inverse spatial metric, then we define \(\bar{\gamma}^{ij} = \phi^{-2} \gamma^{ij}\).