Z4co: add README to wolfram

EinsteinToolkit · Jul 1, 2024 · 8150ad0 · 8150ad0
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diff --git a/Z4co/wolfram/README.md b/Z4co/wolfram/README.md
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+# Z4c
+
+$$
+\begin{align}
+\Gamma^{k}{}_{ij}
+&=\frac{1}{2}\gamma^{kl}(\partial_i\gamma_{jl}+\partial_j\gamma_{li}-\partial_l\gamma_{ij})
+\\
+&=\frac{1}{2}\tilde\gamma^{kl}
+\left[
+  (\partial_i\tilde\gamma_{jl}-\partial_i\ln\chi\tilde\gamma_{jl})+
+  (\partial_j\tilde\gamma_{li}-\partial_j\ln\chi\tilde\gamma_{li})-
+  (\partial_l\tilde\gamma_{ij}-\partial_l\ln\chi\tilde\gamma_{ij})
+\right]
+\\
+&=\tilde\Gamma^k{}_{ij}
+-\frac{1}{2}
+(\partial_i\ln\chi\delta^k{}_j+\partial_j\ln\chi\delta^k{}_i
+-\tilde\gamma_{ij}\tilde\gamma^{kl}\partial_l\ln\chi)
+\end{align}
+$$
+where
+$\partial_l\gamma_{ij}=\partial_l(\chi^{-1}\tilde\gamma_{ij})
+=\chi^{-1}(\partial_l\tilde{\gamma}_{ij}-\chi^{-1}\partial_l\chi\tilde\gamma_{ij})
+=\chi^{-1}(\partial_l\tilde{\gamma}_{ij}-\partial_l\ln\chi\tilde\gamma_{ij})$.