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update: auto commit

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Yingjie Wang
2026-04-10 01:19:11 -04:00
parent 68a93429a6
commit 85b57fb9ba
1 changed files with 1 additions and 4 deletions
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report.tex
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@@ -714,10 +714,7 @@ $}
\[ \[
\scalebox{0.6}{$\displaystyle \scalebox{0.6}{$\displaystyle
\begin{aligned} \begin{aligned}
\pt \chi ={}& \frac{2}{3} \chi \left[ \alpha \left( \hat{K} + \pt \chi ={}&\frac{2}{3} \chi \left[ \alpha \left( \hat{K} +
2\Theta \right) - \dshift{^i_i} - \left( \Gam*{^j_j_k} -
\frac{3}{2} \dchi*{_k} \right) \shift{^k} \right] \notag \\
={}&\frac{2}{3} \chi \left[ \alpha \left( \hat{K} +
2\Theta \right) - \dshift{^i_i} - \Gam*{^j_j_k} \shift{^k} \right] 2\Theta \right) - \dshift{^i_i} - \Gam*{^j_j_k} \shift{^k} \right]
+ \shift{^k} \Partial{_k} \chi,\\ + \shift{^k} \Partial{_k} \chi,\\
\pt \smetric*{_i_j} ={} & - 2 \lapse \Ktf*{_i_j} + \shift{^k} \pt \smetric*{_i_j} ={} & - 2 \lapse \Ktf*{_i_j} + \shift{^k}