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.