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\item Z4 and GH evolve the physical metric, and thus not compatible with the moving puncture method.
\item The rests are using the conformal metric.
\begin{itemize}
\item Z4c and CCZ4 are modifications of Z4, introducing the conformal metric from BSSN to Z4, and damping both the momentum and Hamiltonian constraints.
\item Z4c is simpler than CCZ4. Moreover, it controls the constraints very well in many tests in the community.
\item Z4c damps the constraints better than BSSN, especially in long term evolutions.
\item Unstable in CCZ4 for black hole spacetime was reported.
\end{itemize}
\end{itemize}
\end{frame}