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Yingjie Wang
2026-04-10 01:03:11 -04:00
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@@ -657,7 +657,7 @@
\begin{frame}{Searching for a first order Z4c}{old workflow: by hand} \begin{frame}{Searching for a first order Z4c}{old workflow: by hand}
\subsection{old workflow: by hand} \subsection{old workflow: by hand}
Here is the Z4c evolution system: Here is the Z4c evolution system with the puncture gauge condition:
\[ \[
\scalebox{0.6}{$\displaystyle \scalebox{0.6}{$\displaystyle
\begin{aligned} \begin{aligned}
@@ -691,6 +691,9 @@
\Ktf*{^i^j} + \frac{2}{3} \left( \hat{K} + 2 \Theta \right)^2 \Ktf*{^i^j} + \frac{2}{3} \left( \hat{K} + 2 \Theta \right)^2
\right] - \lapse \left[ 8 \pi \rho + \kappa_1 (2+\kappa_2) \Theta \right] - \lapse \left[ 8 \pi \rho + \kappa_1 (2+\kappa_2) \Theta
\right] + \shift{^i} \Partial{_i} \Theta, \right] + \shift{^i} \Partial{_i} \Theta,
\pt \lapse &= - \mu_L \lapse^2 \hat{K} + \Ld{\beta} \lapse,\\
\pt \shift{^i} &= \mu_S \lapse^2 \Gam*{^i} - \eta \shift{^i} +
\shift{^j} \Partial{_j} \shift{^i}.
\end{aligned} \end{aligned}
$} $}
\] \]