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}