update: auto commit
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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 spical 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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