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Yingjie Wang
2026-04-09 23:57:03 -04:00
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@@ -240,7 +240,7 @@
\begin{frame}{Searching for a first order Z4c}{Why Z4c?}
\section{Searching for a first order Z4c}
\subsection{Why Z4c?}
Let's look at the relationship between different mainly used formulations of Einstein's equations:
% Let's look at the relationship between different mainly used formulations of Einstein's equations:
\begin{figure}
\centering
\begin{tikzpicture}[
@@ -281,7 +281,7 @@
% \node[draw=none, above=1mm of gh, font=\scriptsize] {full first order};
\end{tikzpicture}
\caption{Evolution systems. Second order systems are in blue, and first order systems are in red. Solid arrows represent direct modifications, while dashed arrows represent relation. Dotted bidirectional arrows represent equivalence between systems.}
\caption{Evolution systems. Blue: second order systems; red: first order systems. Solid arrows: direct modifications; dashed arrows: relation. Bidirectional arrows: equivalence between systems.}
\end{figure}
\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.