The conformal longitudinal operator applied to the background shift vector minus the time derivative of the conformal metric $(\bar{L} β_{b a c k g r o u n d})^{i j} - {\bar{u}}^{i j}$ . 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 $(\bar{L} β_{b a c k g r o u n d})^{i j} - {\bar{u}}^{i j}$ .

This quantity appears in formulation of the XCTS equations (see Xcts) and serves to specify their free data ${\bar{u}}_{i j}$ . 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: ${\bar{u}}^{i j} = {\bar{γ}}^{i k} {\bar{γ}}^{j l} \partial_{t} {\bar{γ}}_{k l}$ .

See also: Xcts::Tags::ShiftBackground

The documentation for this struct was generated from the following file:

src/Elliptic/Systems/Xcts/Tags.hpp

Public Types

Detailed Description