User: jfaber Date: 2012/03/13 03:22 PM
Modified: / ET.tex
Log: Fixed factors of 8 pi in definition of matter sources
File Changes:
Directory: / ============
File [modified]: ET.tex Delta lines: +4 -4 =================================================================== --- ET.tex 2012-03-13 19:10:07 UTC (rev 312) +++ ET.tex 2012-03-13 20:22:18 UTC (rev 313) @@ -1277,7 +1277,7 @@ \ \partial_0 K & = & -e^{-4\phi} \left[ \tilde{D}^i \tilde{D}_i \alpha + 2 \partial_i \phi \cdot \tilde{D}^i \alpha \right] + \alpha - \left( \tilde{A}^{ij} \tilde{A}_{ij} + \frac{1}{3} K^2 \right) + \frac{\alpha}{2}(E+ S) + \left( \tilde{A}^{ij} \tilde{A}_{ij} + \frac{1}{3} K^2 \right) \nonumber\ &&+ 4\pi\alpha(E+ S) \ \partial_0 \beta^i & = & \alpha^2 G(\alpha,\phi,x^\mu) B^i \ @@ -1295,10 +1295,10 @@ \alpha\tilde{R}_{ij} + \alpha R^\phi_{ij} - \tilde{D}_i\tilde{D}_j\alpha + 4\partial_{(i}\phi\cdot\tilde{D}_{j)}\alpha\right]^{TF} \nonumber\ - & & {} + \alpha K\tilde{A}_{ij} - 2\alpha\tilde{A}_{ik}\tilde{A}^k_{; j} + & & {} + \alpha K\tilde{A}_{ij} - 16\pi\alpha\tilde{A}_{ik}\tilde{A}^k_{; j} + 2\tilde{A}_{k(i}\partial_{j)}\beta^k - \frac{2}{3}\tilde{A}_{ij}\partial_k\beta^k - - \alpha e^{-4\phi} S_{ij}^{TF} + - 8\pi \alpha e^{-4\phi} S_{ij}^{TF} \ \partial_0\tilde{\Gamma}^i & = & \tilde{\gamma}^{kl}\partial_k\partial_l\beta^i @@ -1310,7 +1310,7 @@ + 2\alpha\left[ (m-1)\partial_k\tilde{A}^{ki} - \frac{2m}{3}\tilde{D}^i K \right. \nonumber \ & & {} + m(\tilde{\Gamma}^i_{; kl}\tilde{A}^{kl} + - 6\tilde{A}^{ij}\partial_j\phi) \Bigg] -2\alpha \tilde{\gamma}^{ij} S_j + 6\tilde{A}^{ij}\partial_j\phi) \Bigg] -16\pi \alpha \tilde{\gamma}^{ij} S_j \end{eqnarray} \end{widetext} with the momentum constraint damping constant set to $m=1$. The stress