Tags related to the XCTS equations. More...
Classes | |
| struct | Conformal |
The quantity Tag scaled by the Xcts::Tags::ConformalFactor to the given Power More... | |
| struct | ConformalChristoffelContracted |
| The Christoffel symbols of the second kind (related to the conformal metric \(\bar{\gamma}_{ij}\)) contracted in their first two indices: \(\bar{\Gamma}_k = \bar{\Gamma}^{i}_{ik}\). More... | |
| struct | ConformalChristoffelFirstKind |
| The Christoffel symbols of the first kind related to the conformal metric \(\bar{\gamma}_{ij}\). More... | |
| struct | ConformalChristoffelSecondKind |
| The Christoffel symbols of the second kind related to the conformal metric \(\bar{\gamma}_{ij}\). More... | |
| struct | ConformalFactor |
| The conformal factor \(\psi(x)\) that rescales the spatial metric \(\gamma_{ij}=\psi^4\bar{\gamma}_{ij}\). More... | |
| struct | ConformalRicciScalar |
| The Ricci scalar related to the conformal metric \(\bar{\gamma}_{ij}\). More... | |
| struct | ConformalRicciTensor |
| The Ricci tensor related to the conformal metric \(\bar{\gamma}_{ij}\). More... | |
| struct | LapseTimesConformalFactor |
| The product of lapse \(\alpha(x)\) and conformal factor \(\psi(x)\). More... | |
| struct | LongitudinalShiftBackgroundMinusDtConformalMetric |
| The conformal longitudinal operator applied to the background shift vector minus the time derivative of the conformal metric \((\bar{L}\beta_\mathrm{background})^{ij} - \bar{u}^{ij}\). More... | |
| struct | LongitudinalShiftExcess |
| The conformal longitudinal operator applied to the shift excess \((\bar{L}\beta_\mathrm{excess})^{ij}\). More... | |
| struct | LongitudinalShiftMinusDtConformalMetricOverLapseSquare |
| The conformal longitudinal operator applied to the shift vector minus the time derivative of the conformal metric, squared and divided by the square of the lapse: \(\frac{1}{\alpha^2}\left((\bar{L}\beta)^{ij} - \bar{u}^{ij}\right) \left((\bar{L}\beta)_{ij} - \bar{u}_{ij}\right)\). More... | |
| struct | LongitudinalShiftMinusDtConformalMetricSquare |
| The conformal longitudinal operator applied to the shift vector minus the time derivative of the conformal metric, squared: \(\left((\bar{L}\beta)^{ij} - \bar{u}^{ij}\right) \left((\bar{L}\beta)_{ij} - \bar{u}_{ij}\right)\). More... | |
| struct | ShiftBackground |
| The constant part \(\beta^i_\mathrm{background}\) of the shift \(\beta^i=\beta^i_\mathrm{background} + \beta^i_\mathrm{excess}\). More... | |
| struct | ShiftDotDerivExtrinsicCurvatureTrace |
| The shift vector contracted with the gradient of the trace of the extrinsic curvature: \(\beta^i\partial_i K\). More... | |
| struct | ShiftExcess |
| The dynamic part \(\beta^i_\mathrm{excess}\) of the shift \(\beta^i=\beta^i_\mathrm{background} + \beta^i_\mathrm{excess}\). More... | |
| struct | ShiftStrain |
| The symmetric "strain" of the shift vector \(B_{ij} = \bar{D}_{(i}\bar{\gamma}_{j)k}\beta^k = \left(\partial_{(i}\bar{\gamma}_{j)k} - \bar{\Gamma}_{kij}\right)\beta^k\). More... | |
Typedefs | |
| template<typename DataType , size_t Dim, typename Frame > | |
| using | ConformalMetric = Conformal< gr::Tags::SpatialMetric< Dim, Frame, DataType >, -4 > |
The conformally scaled spatial metric \(\bar{\gamma}_{ij}=\psi^{-4}\gamma_{ij}\), where \(\psi\) is the Xcts::Tags::ConformalFactor and \(\gamma_{ij}\) is the gr::Tags::SpatialMetric | |
| template<typename DataType , size_t Dim, typename Frame > | |
| using | InverseConformalMetric = Conformal< gr::Tags::InverseSpatialMetric< Dim, Frame, DataType >, 4 > |
The conformally scaled inverse spatial metric \(\bar{\gamma}^{ij}=\psi^{4}\gamma^{ij}\), where \(\psi\) is the Xcts::Tags::ConformalFactor and \(\gamma^{ij}\) is the gr::Tags::InverseSpatialMetric | |
Tags related to the XCTS equations.