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,