[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 282)

[roland.haas at physics.gatech.edu]

User: rhaas
Date: 2012/03/12 10:38 AM

Modified:
 /
  ET.tex

Log:
 remove offending sentence below Equ. 15 wrt to origin handling in TOV solver

File Changes:

Directory: /
============

File [modified]: ET.tex
Delta lines: +2 -3
===================================================================
--- ET.tex	2012-03-12 15:37:20 UTC (rev 281)
+++ ET.tex	2012-03-12 15:38:08 UTC (rev 282)
@@ -1112,7 +1112,7 @@
 The routine also supplies the analytically known 
 solution in the exterior,
 \begin{eqnarray}
-     P & = & P({\tt TOV\_atmosphere}),\nonumber \\
+     P & = & P(\mbox{\tt TOV\_atmosphere}),\nonumber \\
      M_e & = & M, \nonumber\\
   \Phi & = &\dfrac{1}{2} \log(1-2M / \hat{r})
   \label{eq:TOVexterior}
@@ -1129,9 +1129,8 @@
 subject to the boundary condition that in the exterior,
 \begin{eqnarray}
 r &=& \dfrac{1}{2}\left(\sqrt{\hat{r}^2-2Mr}+\hat{r} -M\right)\nonumber \\
-\hat{r}&=&r\left(1+\dfrac{M}{2r}\right)^2 \ ,
+\hat{r}&=&r\left(1+\dfrac{M}{2r}\right)^2 \ .
 \end{eqnarray}
-handling with some care the potentially singular terms that appear at the origin.
 In converting the solution into the variables required for a dynamical evolution, one may assume that the metric is conformally flat, with a conformal factor given by $\psi = \sqrt{\hat{r}/r}$, or equivalently, a logarithmic conformal factor $\phi = \frac{1}{2}\log(\hat{r}/r)$.
 
 To facilitate the construction of stars in more complicated dynamical configurations,