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