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