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SpECTRE
v2024.04.12
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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 > |
The spatial derivative of the conformal spatial christoffel symbols of the second kind.
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.