[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 309)

[jfaber at einsteintoolkit.org]

User: jfaber
Date: 2012/03/13 11:15 AM

Modified:
 /
  ET.tex

Log:
 Fixed the description in to TOVSolver footnote about notation; no footnote necessary

File Changes:

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

File [modified]: ET.tex
Delta lines: +5 -5
===================================================================
--- ET.tex	2012-03-13 15:14:05 UTC (rev 308)
+++ ET.tex	2012-03-13 16:15:16 UTC (rev 309)
@@ -710,7 +710,7 @@
 $K_{ij}$ & Extrinsic curvature & \protect\ref{eq:extrcurv} & ADMBase::curv\\
 $\rho$ & Rest mass density & \protect\ref{eq:Tmunu},\protect\ref{eq:enthalpy} & HydroBase::rho\\
 $P$ & Fluid pressure & \protect\ref{eq:enthalpy} & HydroBase::press\\
-$\epsilon$ & Internal energy density & \protect\ref{eq:enthalpy} & Hydrobase::eps\\
+$\epsilon$ & Specific internal energy & \protect\ref{eq:enthalpy} & Hydrobase::eps\\
 $h$ & Specific enthalpy & \protect\ref{eq:enthalpy} & N/A\\
 $v^i$ & 3-velocity & \protect\ref{eq:3vel} & HydroBase::vel\\
 $B^i$ & Magnetic field vector & \protect\ref{eq:Bi} & HydroBase::Bvec\\
@@ -884,7 +884,7 @@
 \begin{itemize}
  \item \verb|rho|: rest mass density $\rho$
  \item \verb|press|: pressure $P$
- \item \verb|eps|: internal energy density $\epsilon$
+ \item \verb|eps|: Specific internal energy $\epsilon$
  \item \verb|vel[3]|: contravariant fluid three velocity $v^i$ defined as
   \begin{equation}
       v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha}\label{eq:3vel}
@@ -1116,14 +1116,14 @@
 radius $\hat{r}$:
 \begin{eqnarray}
   \label{eq:TOViso}
-  \frac{d P}{d \hat{r}} & = & -(e + P) \frac{M_e + 4\pi \hat{r}^3 P}{\hat{r}(\hat{r} - 2M_e)}\nonumber\\
+  \frac{d P}{d \hat{r}} & = & -(\mu + P) \frac{M_e + 4\pi \hat{r}^3 P}{\hat{r}(\hat{r} - 2M_e)}\nonumber\\
 %
-  \frac{d M_e}{d \hat{r}} & = & 4 \pi \hat{r}^2 e\nonumber\\
+  \frac{d M_e}{d \hat{r}} & = & 4 \pi \hat{r}^2 \mu\nonumber\\
 %
   \frac{d \Phi}{d \hat{r}} & = & \frac{M_e + 4\pi \hat{r}^3 P}{\hat{r}(\hat{r} -
     2M_e)}.
 \end{eqnarray}
-where $e\equiv \rho(1+\epsilon)$ is the energy density of the fluid, including the internal energy contribution\footnote[1]{We note that since different application thorns may define their own local variables, the energy density is referred to as {\tt rho} within \codename{TOVSolver}, as the projected energy density $E$, defined in Sec.~\protect\ref{sec:Kevol}, is within \codename{McLachlan} and a few other thorns.  Similar ambiguities exist for other commonly used variable names, particularly $\phi$ and $\alpha$.}.
+where $\mu\equiv \rho(1+\epsilon)$ is the energy density of the fluid, including the internal energy contribution.
 The routine also supplies the analytically known 
 solution in the exterior,
 \begin{eqnarray}