SpECTRE  v2021.12.06
Ccz4::Tags::ChristoffelSecondKind< Dim, Frame, DataType > Struct Template Reference

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

#include <Tags.hpp>

Public Types

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

Detailed Description

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

The spatial christoffel symbols of the second kind.

Details

We define:

\begin{align} \Gamma^k_{ij} &= \tilde{\Gamma}^k_{ij} - \tilde{\gamma}^{kl} (\tilde{\gamma}_{jl} P_i + \tilde{\gamma}_{il} P_j - \tilde{\gamma}_{ij} P_l) \end{align}

where \(\tilde{\gamma}^{ij}\), \(\tilde{\gamma}_{ij}\), \(\tilde{\Gamma}^k_{ij}\), and \(P_i\) are the conformal spatial metric, the inverse conformal spatial metric, the conformal spatial christoffel symbols of the second kind, and the CCZ4 auxiliary variable defined by Ccz4::Tags::ConformalMetric, Ccz4::Tags::InverseConformalMetric, Ccz4::Tags::ConformalChristoffelSecondKind, and Ccz4::Tags::FieldP, respectively.


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