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.