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update: auto commit

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Yingjie Wang
2026-04-10 01:04:52 -04:00
parent 2c984734ce
commit f4feaee88d
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@@ -666,7 +666,7 @@
\pt \smetric*{_i_j} ={} & - 2 \lapse \Ktf*{_i_j} + \shift{^k} \pt \smetric*{_i_j} ={} & - 2 \lapse \Ktf*{_i_j} + \shift{^k}
\Partial{_k} \smetric*{_i_j} + 2 \smetric*{_{k(i}} \Partial{_{j)}} \Partial{_k} \smetric*{_i_j} + 2 \smetric*{_{k(i}} \Partial{_{j)}}
\shift{^k} - \frac{2}{3} \smetric*{_i_j} \Partial{_k} \shift{^k},\\ \shift{^k} - \frac{2}{3} \smetric*{_i_j} \Partial{_k} \shift{^k},\\
\pt \hat{K} ={}& - \spaceD{^i} \spaceD{_i} \lapse + \lapse \left[ \pt \hat{K} ={}& - {\color{red}\spaceD{^i} \spaceD{_i} \lapse} + \lapse \left[
\Ktf*{_i_j} \Ktf*{^i^j} + \frac{1}{3} \left( \hat{K} + 2 \Theta \Ktf*{_i_j} \Ktf*{^i^j} + \frac{1}{3} \left( \hat{K} + 2 \Theta
\right)^2 \right] + 4 \pi \lapse \left( S + \rho \right) + \lapse \right)^2 \right] + 4 \pi \lapse \left( S + \rho \right) + \lapse
\kappa_1 (1-\kappa_2) \Theta + \shift{^i} \Partial{_i} \hat{K},\\ \kappa_1 (1-\kappa_2) \Theta + \shift{^i} \Partial{_i} \hat{K},\\