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Yingjie Wang
2026-04-10 00:00:29 -04:00
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\caption{Blue: second order systems; red: first order systems. Solid arrows: direct modifications; dashed arrows: relation. Bidirectional arrows: equivalence between systems.} \caption{Blue: second order systems; red: first order systems. Solid arrows: direct modifications; dashed arrows: relation. Bidirectional arrows: equivalence between systems.}
\end{figure} \end{figure}
\begin{itemize} \begin{itemize}
\item Z4 and GH are said to be equivalent. They damps the momentum constraint and the Hamiltonian constraint respectively. They evolve the physical metric, and thus not compatible with the moving puncture method. \item Z4 and GH are said to be equivalent. They damps the GR constraints. They evolve the physical metric, and thus not compatible with the moving puncture method.
\item The rests are using the conformal metric, and thus compatible with the moving puncture method. \item The rests are using the conformal metric, and thus compatible with the moving puncture method.
\begin{itemize} \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 and CCZ4 are modifications of Z4, introducing the conformal metric from BSSN to Z4, and damping both the momentum and Hamiltonian constraints.