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update: auto commit

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Yingjie Wang
2026-04-10 01:07:28 -04:00
parent 02ef83bbe8
commit 3d1fe81fe5
1 changed files with 3 additions and 3 deletions
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report.tex
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@@ -681,9 +681,9 @@
\left[ \Gam*{^i_j_k} \Ktf*{^j^k} - \frac{3}{2} \Ktf*{^i^j} \left[ \Gam*{^i_j_k} \Ktf*{^j^k} - \frac{3}{2} \Ktf*{^i^j}
\Partial{_j} \ln(\chi) - \frac{1}{3} \smetric*{^i^j} \Partial{_j} \Partial{_j} \ln(\chi) - \frac{1}{3} \smetric*{^i^j} \Partial{_j}
\left( 2 \hat{K} + \Theta \right) - 8 \pi \smetric*{^i^j} \left( 2 \hat{K} + \Theta \right) - 8 \pi \smetric*{^i^j}
\tensor{S}{_j} \right] + \smetric*{^j^k} \Partial{_j} \Partial{_k} \tensor{S}{_j} \right] + {\color{red}\smetric*{^j^k} \Partial{_j} \Partial{_k} \shift{^i}}
\shift{^i} + \frac{1}{3} \smetric*{^i^j} \Partial{_j} \Partial{_k} + {\color{red}\frac{1}{3} \smetric*{^i^j} \Partial{_j} \Partial{_k}
\shift{^k} \notag\\ \shift{^k}} \notag\\
& {} + \shift{^j} \Partial{_j} \Gam*{^i} - \Gamd*{^j} \Partial{_j} & {} + \shift{^j} \Partial{_j} \Gam*{^i} - \Gamd*{^j} \Partial{_j}
\shift{^i} + \frac{2}{3} \Gamd*{^i} \Partial{_j} \shift{^j} - 2 \shift{^i} + \frac{2}{3} \Gamd*{^i} \Partial{_j} \shift{^j} - 2
\lapse \kappa_1 \left[ \Gam*{^i} - \Gamd*{^i} \right], \\ \lapse \kappa_1 \left[ \Gam*{^i} - \Gamd*{^i} \right], \\