Xcts::Tags Namespace Reference

Tags related to the XCTS equations. More...

Classes
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	ConformalFactorMinusOne
	The conformal factor minus one \(\psi(x) - 1\). Useful as dynamic variable in formulations of the XCTS equations because it approaches zero at spatial infinity rather than one, hence derivatives may be more accurate. 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	HydroQuantitiesCompute
	MHD quantities retrieved from the background solution/data. More...
struct	LapseTimesConformalFactor
	The product of lapse \(\alpha(x)\) and conformal factor \(\psi(x)\). More...
struct	LapseTimesConformalFactorMinusOne
	The lapse times the conformal factor minus one \(\alpha \psi - 1\). 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...
struct	SpacetimeQuantitiesCompute
	Compute tag for the 3+1 quantities Tags from XCTS variables. The Tags can be any subset of the tags supported by Xcts::SpacetimeQuantities. More...

Typedefs
template<typename DataType , size_t Dim, typename Frame >
using	ConformalMetric = gr::Tags::Conformal< gr::Tags::SpatialMetric< DataType, Dim, Frame >, -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 = gr::Tags::Conformal< gr::Tags::InverseSpatialMetric< DataType, Dim, Frame >, 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.