[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 213)

[schnetter at cct.lsu.edu]

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

Modified:
 /
  ET.tex

Log:
 Reword

File Changes:

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}