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SpECTRE
v2025.04.21
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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 | ATildeMinusOneThirdConformalMetricTimesTraceATilde |
| The CCZ4 temporary expression \(\tilde{A}_{ij} - \frac{1}{3} \tilde{\gamma}_{ij} tr \tilde{A}\). More... | |
| struct | ATildeTimesFieldB |
| The CCZ4 temporary expression \( \tilde{A}_{ki}\partial_j\beta^k \). More... | |
| struct | AuxiliaryShiftB |
| Auxiliary variable b in the gamma-driver condition eq. 12c of [66]. 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 | ConformalMetricTimesFieldB |
| The CCZ4 temporary expression \(\tilde{\gamma}_{ki} B_j{}^k\). More... | |
| struct | ConformalMetricTimesTraceATilde |
| The CCZ4 temporary expression \(\tilde{\gamma}_{ij} tr \tilde{A}\). More... | |
| struct | ContractedChristoffelSecondKind |
| The CCZ4 temporary expression \( \Gamma^k_{ik} \). More... | |
| struct | ContractedConformalChristoffelSecondKind |
| The contraction of the conformal spatial Christoffel symbols of the second kind. More... | |
| struct | ContractedDerivConformalChristoffelDifference |
| The CCZ4 temporary expression \( \partial_m\tilde{\Gamma}^m_{ij}-\partial_j\tilde{Gamma}^m_{im} \). More... | |
| struct | ContractedFieldB |
| The CCZ4 temporary expression \(B_k{}^k\). More... | |
| struct | ContractedFieldDUp |
| The CCZ4 temporary expression \( \tilde{\gamma}^{kn}\tilde{\gamma}^{mj}D_{knm} \). More... | |
| struct | ContractedSymmetrizedDerivFieldB |
| The CCZ4 temporary expression \( \partial_k\partial_l\beta^l \). 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 | DerivGammaHatMinusContractedConformalChristoffel |
| The CCZ4 temporary expression \( \hat{\Gamma}^l-\tilde{\Gamma}^l \) in eq. (26) of [66]. More... | |
| struct | DetConformalSpatialMetric |
| The CCZ4 temporary expression ( \( \mathrm{det}\tilde{\gamma}_{ij} \)) More... | |
| struct | DivergenceLapse |
| The divergence of the lapse. More... | |
| struct | Eta |
| The parameter \( \eta \) in the gamma-driver condition eq. 12i of [66]. 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 | FieldDUpTimesATilde |
| The CCZ4 temporary expression \(D_k{}^{nm} \tilde{A}_{nm}\). More... | |
| struct | FieldP |
| Auxiliary variable which is analytically the spatial derivative of the natural log of the conformal factor. More... | |
| struct | GammaDriverParam |
| The parameter f in the gamma-driver condition eq. 12c of [66]. 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 | HalfConformalFactorSquared |
| The CCZ4 temporary expression \( (1/2)\phi^2 \). More... | |
| struct | InvATilde |
| The CCZ4 temporary expression \( \tilde{A}^{ij} \). More... | |
| struct | InverseConformalMetricTimesDerivATilde |
| The CCZ4 temporary expression \(\tilde{\gamma}^{nm} \partial_k \tilde{A}_{nm}\). More... | |
| struct | InverseTauTimesConformalMetric |
| The CCZ4 temporary expression \(\tau^{-1} \tilde{\gamma}_{ij}\). More... | |
| struct | K0 |
| Free parameter \( K_0 \) in 1+log slicing in eq. 12b of [66]. More... | |
| struct | Kappa1 |
| Free parameter \( kappa_1 \) related to constraint damping in eq. 12f of [66]. More... | |
| struct | Kappa2 |
| Free parameter \( kappa_2 \) related to constraint damping in eq. 12f of [66]. More... | |
| struct | Kappa3 |
| Free parameter \( kappa_3 \) related to constraint damping in eq. 12h of [66]. More... | |
| struct | KMinus2ThetaC |
| The CCZ4 temporary expression \(K - 2 \Theta c\). More... | |
| struct | KMinusK0Minus2ThetaC |
| The CCZ4 temporary expression \(K - K_0 - 2 \Theta c\). More... | |
| struct | LapseTimesATilde |
| The CCZ4 temporary expression \(\alpha \tilde{A}_{ij}\). More... | |
| struct | LapseTimesConformalMetric |
| The CCZ4 temporary expression \( \alpha\tilde{\gamma}_{ij} \). More... | |
| struct | LapseTimesDerivATilde |
| The CCZ4 temporary expression \(\alpha \partial_k \tilde{A}_{ij}\). More... | |
| struct | LapseTimesFieldA |
| The CCZ4 temporary expression \(\alpha A_k\). More... | |
| struct | LapseTimesRicciScalarPlus2DivergenceZ4Constraint |
| The CCZ4 temporary expression \(\alpha (R + 2 \nabla_k Z^k)\). More... | |
| struct | LapseTimesSlicingCondition |
| The CCZ4 temporary expression \(\alpha g(\alpha)\). 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 | ShiftTimesDerivGammaHat |
| The CCZ4 temporary expression \(\beta^k \partial_k \hat{\Gamma}^i\). More... | |
| struct | SpatialRicciTensor |
| The CCZ4 temporary expression \( R_{ij} \). More... | |
| struct | SpatialZ4Constraint |
| The spatial part of the Z4 constraint. More... | |
| struct | SpatialZ4ConstraintUp |
| The spatial part of the upper Z4 constraint. More... | |
| struct | SymmetrizedDerivFieldB |
| The CCZ4 temporary expression \( \partial_k\partial_l\beta^i \). More... | |
| struct | Theta |
| The projection of the Z4 constraint vector along the normal direction. More... | |
| struct | TraceATilde |
| The trace of the trace-free part of the extrinsic curvature. More... | |
| struct | UpperSpatialZ4Contraint |
| The CCZ4 temporary expression \( Z^i \). More... | |
Typedefs | |
| template<typename DataType , size_t Dim, typename Fr = Frame::Inertial> | |
| using | ConformalMetric = gr::Tags::Conformal< gr::Tags::SpatialMetric< DataType, Dim, Fr >, 2 > |
| The conformally scaled spatial metric. More... | |
| template<typename DataType , size_t Dim, typename Frame = Frame::Inertial> | |
| using | InverseConformalMetric = gr::Tags::Conformal< gr::Tags::InverseSpatialMetric< DataType, Dim, Frame >, -2 > |
| The conformally scaled inverse spatial metric. More... | |
Tags for the CCZ4 formulation of Einstein equations.
The naming convention follows [66] eq. 12a-12m.
| using Ccz4::Tags::ConformalMetric = typedef gr::Tags::Conformal<gr::Tags::SpatialMetric<DataType, Dim, Fr>, 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<DataType, Dim, Frame>, -2> |
The conformally scaled inverse spatial metric.
If \(\phi\) is the conformal factor and \(\gamma^{ij}\) is the inverse spatial metric, then we define \(\bar{\gamma}^{ij} = \phi^{-2} \gamma^{ij}\).