[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 285)

[roland.haas at physics.gatech.edu]

User: rhaas
Date: 2012/03/12 10:56 AM

Modified:
 /
  ET.tex

Log:
 re-word explanation of why point-wise convergence at origin fails.

File Changes:

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

File [modified]: ET.tex
Delta lines: +4 -6
===================================================================
--- ET.tex	2012-03-12 15:55:18 UTC (rev 284)
+++ ET.tex	2012-03-12 15:56:23 UTC (rev 285)
@@ -2982,12 +2982,10 @@
 violation~\eref{eqn:analysis_hamiltonian_constraint} at the center of
 the collapsing star.
 Up to the time when the apparent horizon forms, the convergence order is
-an expected $\approx 1.5$. At later times, the collapse of the lapse
-function at the
-center of the collapsing star renders a pointwise measurement of the
-convergence factor at the center impossible. Similarly the $\Gamma$-driver
-shift condition used, pushes the infalling matter beyond the
-innermost grid point~\cite{Thierfelder:2010dv}. Eventually the shock
+an expected $\approx 1.5$. At later times the $\Gamma$-driver
+shift condition used pushes the infalling matter beyond the
+innermost grid point~\cite{Thierfelder:2010dv}, which prevents a clean
+measurement of a convergence factor. Eventually the shock
 capturing scheme is unable to resolve the steep gradients and becomes
 dissipative, which leads to a loss of rest mass inside of the apparent
 horizon. The observed horizon mass on the other hand stays constant.