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SpECTRE
v2024.09.16
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The spatial christoffel symbols of the second kind. More...
#include <Tags.hpp>
Public Types | |
| using | type = tnsr::Ijj< DataType, Dim, Frame > |
The spatial christoffel symbols of the second kind.
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.