Xcts::Tags::LongitudinalShiftBackgroundMinusDtConformalMetric< DataType, Dim, Frame > Struct Template Reference

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...

#include <Tags.hpp>

## Public Types

using type = tnsr::II< DataType, Dim, Frame >

## Detailed Description

template<typename DataType, size_t Dim, typename Frame>
struct Xcts::Tags::LongitudinalShiftBackgroundMinusDtConformalMetric< DataType, Dim, Frame >

The conformal longitudinal operator applied to the background shift vector minus the time derivative of the conformal metric $$(\bar{L}\beta_\mathrm{background})^{ij} - \bar{u}^{ij}$$.

This quantity appears in formulation of the XCTS equations (see Xcts) and serves to specify their free data $$\bar{u}_{ij}$$. It is combined with the longitudinal background shift because the two quantities are degenerate.

Note
As usual for conformal quantities, the indices here are raised with the conformal metric: $$\bar{u}^{ij} = \bar{\gamma}^{ik}\bar{\gamma}^{jl} \partial_t\bar{\gamma}_{kl}$$.
Xcts::Tags::ShiftBackground