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update: auto commit

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Yingjie Wang
2026-04-10 01:05:39 -04:00
parent f4feaee88d
commit 35f3122b4c
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@@ -670,7 +670,7 @@
\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},\\
\pt \Ktf*{_i_j} ={} & \chi \left[ - \spaceD{_i} \spaceD{_j} \lapse \pt \Ktf*{_i_j} ={} & \chi \left[ - {\color{red}\spaceD{_i} \spaceD{_j} \lapse}
+ \lapse \left( \Rictensor{_i_j} - 8 \pi \tensor{S}{_i_j} \right) + \lapse \left( \Rictensor{_i_j} - 8 \pi \tensor{S}{_i_j} \right)
\right]^{\text{tf}} + \lapse \left[ \left( \hat{K} + 2 \Theta \right]^{\text{tf}} + \lapse \left[ \left( \hat{K} + 2 \Theta
\right) \Ktf*{_i_j} - 2 \Ktf*{^k_i} \Ktf*{_k_j} \right] + \right) \Ktf*{_i_j} - 2 \Ktf*{^k_i} \Ktf*{_k_j} \right] +