SpECTRE  v2025.04.21
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  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...
 

Detailed Description

Tags for the CCZ4 formulation of Einstein equations.

Details

The naming convention follows [66] eq. 12a-12m.

Typedef Documentation

◆ ConformalMetric

template<typename DataType , size_t Dim, typename Fr = Frame::Inertial>
using Ccz4::Tags::ConformalMetric = typedef gr::Tags::Conformal<gr::Tags::SpatialMetric<DataType, Dim, Fr>, 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<typename DataType , size_t Dim, typename Frame = Frame::Inertial>
using Ccz4::Tags::InverseConformalMetric = typedef gr::Tags::Conformal<gr::Tags::InverseSpatialMetric<DataType, Dim, Frame>, -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 \(\bar{\gamma}^{ij} = \phi^{-2} \gamma^{ij}\).