Classes | Typedefs
Xcts::Tags Namespace Reference

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
 

Detailed Description

Tags related to the XCTS equations.