[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 313)

[jfaber at einsteintoolkit.org]

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