From e1351ce3df7ab8b1e0758cf9584820e74440652b Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 12:26:40 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/report.tex b/report.tex
index 62171ca..3d3e7c3 100644
--- a/report.tex
+++ b/report.tex
@@ -12,6 +12,8 @@
 
 \usepackage{appendixnumberbeamer}
 
+\newcommand{\Schwarzschild}{Schwarzschild}
+
 \tikzset{zigzag/.style={decorate, decoration=zigzag}}
 \def \L {2.}
 
@@ -279,7 +281,7 @@
             -- (2*\L,0.5*\L) node[right,align=left]
             {time slice};
         \end{tikzpicture}
-        \caption{excision on a single Schwarchild black hole}
+        \caption{excision on a single Schwarzschild black hole}
       \end{figure}
   \end{frame}
 
@@ -293,7 +295,7 @@
 
 
   \begin{frame}{Methods on evolving black holes: moving puncture}
-    In the isotropic coordinate for Schwarzschild black hole, the spacial metric
+    In the isotropic coordinate for \Schwarzschild{} black hole, the spacial metric
     \begin{equation}
       \dd{l^2} = \left( 1+\frac{M}{2r} \right)^4 (\dd{r^2} + r^2 \dd{\Omega^2})
     \end{equation}