User: eschnett Date: 2011/11/14 09:40 AM

Modified: / ET.tex

Log: Reword

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

File [modified]: ET.tex Delta lines: +6 -16 =================================================================== --- ET.tex 2011-11-14 15:37:03 UTC (rev 212) +++ ET.tex 2011-11-14 15:40:14 UTC (rev 213) @@ -72,6 +72,8 @@ % You can use a baselinestretch of down to 0.9 %\renewcommand{\baselinestretch}{0.96}

+\hyphenation{Schwarz-schild} + \sloppypar

\begin{document} @@ -2726,23 +2728,11 @@ the apparent horizon that eventually forms in the simulation. The apparent horizon is first found at approximately the time when the star's coordinate radius approaches its Schwarzschild radius, though -one ought to keep in mind that the Schwarzschild radius is a +one needs to keep in mind that the Schwarzschild radius is a circumferential radius, whereas the meaning of the coordinate radius -in our BSSN calculation is closer to a radius in isotropic gauge -\todo{Roland, do you agree?}. -\todo{RH: TOVSolver sets up isotropic coordinates initially, at the end of the -simulation though I have sizeable off-diagonal metric components (gxy is about -0.2 within 6M) and also a non-zero shift, the metric diagonal elements are also not -idenical. So the coordinate system is no longer obviously isotropic as far as I -can tell. On the other hand it is also not just Schwarzschild coordinates -transformed to Cartesian coordinates using the flat space expressions for r, -$\theta$ and $\phi$. So I -agree the the coordinates are likely not Schwarzschild coordinates but am not -sure that they are still isotropic since the direction towards the center is -special. So I'd add a weaker statement ``\ldots in our BSSN calculation is not -necessarily that of a circumferential radius''} - In Figure~\ref{fig:tov_collapse_H_convergence_at0}, we display the - convergence factor obtained from +in our BSSN calculation is likely somewhat different. +In Figure~\ref{fig:tov_collapse_H_convergence_at0}, we display the +convergence factor obtained from \begin{equation} \frac{H_{h_1}-H_{h_2}}{H_{h_2}-H_{h_3}} = \frac{h_1^Q-h_2^Q}{h_2^Q-h_3^Q},, \label{eq:convergence-factor-definition}