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update: auto commit

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Yingjie Wang
2026-04-10 01:03:34 -04:00
parent 1b72bcdfd9
commit 2c984734ce
1 changed files with 3 additions and 3 deletions
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report.tex
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@@ -690,9 +690,9 @@
\pt \Theta ={} & \frac{1}{2} \lapse \left[ \Rscalar - \Ktf*{_i_j} \pt \Theta ={} & \frac{1}{2} \lapse \left[ \Rscalar - \Ktf*{_i_j}
\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 \lapse ={} & - \mu_L \lapse^2 \hat{K} + \Ld{\beta} \lapse,\\
\pt \shift{^i} &= \mu_S \lapse^2 \Gam*{^i} - \eta \shift{^i} + \pt \shift{^i} ={} & \mu_S \lapse^2 \Gam*{^i} - \eta \shift{^i} +
\shift{^j} \Partial{_j} \shift{^i}. \shift{^j} \Partial{_j} \shift{^i}.
\end{aligned} \end{aligned}
$} $}