From 27cc012c84955c78a4bdbfb7581a5076307531f8 Mon Sep 17 00:00:00 2001 From: Yingjie Wang Date: Fri, 10 Apr 2026 12:58:59 -0400 Subject: [PATCH] update: auto commit --- report.tex | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/report.tex b/report.tex index afc57df..b15adb9 100644 --- a/report.tex +++ b/report.tex @@ -238,15 +238,17 @@ \end{frame} \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: \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. \end{itemize} \end{frame} \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} \centering \begin{tikzpicture}[>=Latex, line cap=round, line join=round] @@ -288,6 +290,7 @@ \end{frame} \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} \centering \includegraphics[width=0.7\textwidth]{imgs/black_hole_excision_mesh.png} @@ -297,6 +300,8 @@ \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 \begin{equation} \dd{l^2} = \left( 1+\frac{M}{2r} \right)^4 (\dd{r^2} + r^2 \dd{\Omega^2})