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Yingjie Wang
2026-04-10 12:58:59 -04:00
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\end{frame} \end{frame}
\begin{frame}{Methods on evolving black holes} \begin{frame}{Methods on evolving black holes}
\subsection{Methods on evolving black holes}
There are two main methods to evolve black holes in numerical relativity: There are two main methods to evolve black holes in numerical relativity:
\begin{itemize} \begin{itemize}
\item Excision method: excise the black hole interior from the computational domain, and impose boundary conditions on the excision surface \item
\item Moving puncture method: evolve the black hole as a puncture, and use a suitable gauge condition to avoid the singularity. \item Moving puncture method: evolve the black hole as a puncture, and use a suitable gauge condition to avoid the singularity.
\end{itemize} \end{itemize}
\end{frame} \end{frame}
\begin{frame}{Methods on evolving black holes: excision} \begin{frame}{Methods on evolving black holes: excision}
\subsection{Methods on evolving black holes}
Excision method: excise the black hole interior from the computational domain, and impose boundary conditions on the excision surface.
\begin{figure} \begin{figure}
\centering \centering
\begin{tikzpicture}[>=Latex, line cap=round, line join=round] \begin{tikzpicture}[>=Latex, line cap=round, line join=round]
@@ -288,6 +290,7 @@
\end{frame} \end{frame}
\begin{frame}{Methods on evolving black holes: excision} \begin{frame}{Methods on evolving black holes: excision}
Excision method: excise the black hole interior from the computational domain, and impose boundary conditions on the excision surface
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=0.7\textwidth]{imgs/black_hole_excision_mesh.png} \includegraphics[width=0.7\textwidth]{imgs/black_hole_excision_mesh.png}
@@ -297,6 +300,8 @@
\begin{frame}{Methods on evolving black holes: moving puncture} \begin{frame}{Methods on evolving black holes: moving puncture}
Moving puncture method: use a suitable gauge condition to make sure the singularity is not on our time slices at all.
In the isotropic coordinate for Schwarzschild black hole, the spatial metric In the isotropic coordinate for Schwarzschild black hole, the spatial metric
\begin{equation} \begin{equation}
\dd{l^2} = \left( 1+\frac{M}{2r} \right)^4 (\dd{r^2} + r^2 \dd{\Omega^2}) \dd{l^2} = \left( 1+\frac{M}{2r} \right)^4 (\dd{r^2} + r^2 \dd{\Omega^2})