SpECTRE  v2021.12.06
Ccz4::Tags::DerivConformalChristoffelSecondKind< Dim, Frame, DataType > 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<size_t Dim, typename Frame, typename DataType>
struct Ccz4::Tags::DerivConformalChristoffelSecondKind< Dim, Frame, DataType >

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

Details

We define:

\begin{align} \partial_k \tilde{\Gamma}^m{}_{ij} &= -2 D_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{align}

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.


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