Ccz4::Tags::DerivConformalChristoffelSecondKind< DataType, Dim, Frame > Struct Template Reference

The spatial derivative of the conformal spatial christoffel symbols of the second kind. More...

#include <Tags.hpp>

Public Types
using	type = tnsr::iJkk< DataType, Dim, Frame >

Detailed Description

template<typename DataType, size_t Dim, typename Frame>
struct Ccz4::Tags::DerivConformalChristoffelSecondKind< DataType, Dim, Frame >

The spatial derivative of the conformal spatial christoffel symbols of the second kind.

Details

We define:

$$\begin{array}{}\text{(1)}& {\partial }_k{\tilde{\mathrm{\Gamma }}}^m{}_{ij}& =-2D_k{}^{ml}(D_{ijl}+D_{jil}-D_{lij})+{\tilde{\gamma }}^{ml}({\partial }_{(k}{D}_{i)jl}+{\partial }_{(k}{D}_{j)il}-{\partial }_{(k}{D}_{l)ij})\end{array}$$

where ${\tilde{\gamma }}^{ij}$, $D_{ijk}$, ${\partial }_l{D}_{ijk}$, and $D_k{}^{ij}$ are the inverse conformal spatial metric defined by Ccz4::Tags::InverseConformalMetric, the CCZ4 auxiliary variable defined by Ccz4::Tags::FieldD, its spatial derivative, and the CCZ4 identity defined by Ccz4::Tags::FieldDUp.

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

• src/Evolution/Systems/Ccz4/Tags.hpp