[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 188)

[roland.haas at physics.gatech.edu]

User: rhaas
Date: 2011/11/11 06:34 PM

Modified:
 /
  ET.tex

Log:
 define quantities in ns collapse
 add some comments wrt Christian comments
 start working (from the end) on the issues in ETcomments.pdf

File Changes:

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

File [modified]: ET.tex
Delta lines: +18 -4
===================================================================
--- ET.tex	2011-11-11 21:06:36 UTC (rev 187)
+++ ET.tex	2011-11-12 00:34:24 UTC (rev 188)
@@ -539,6 +539,8 @@
 
 The Simulation Factory supports and simplifies three kinds of
 operations:
+%RH: any of the itemize, decription, enumerate environments indents its body
+%by the same amount as \parindent
 \begin{description}
 \item[Remote Access] The actual access commands and authentication
   methods differ between systems, as do the user names that a person
@@ -2681,7 +2683,7 @@
 polytropic constant $K_{\mathrm{ID}}$ from its initial value to
 $K = 0.98 \, K_{\mathrm{ID}} = 98$.  To ensure that the pressure
 depleted configuration remains a solution of the Einstein constraint
-equations (Eq.~\ref{eqn:analysis_hamiltonian_constraint}) in the presence
+equations~\eref{eqn:analysis_hamiltonian_constraint} in the presence
 of matter we rescale the rest mass density $\rho$ such that the total
 energy density $T_{nn}$
 %\todo{RH: unify notation of $\rho$} 
@@ -2752,15 +2754,27 @@
 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
 \begin{equation}
-    Q = \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}\,,
+    \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}
 \end{equation}
-where ... \todo{Roland, define H, h and subscripts}
 for the Hamiltonian constraint violation at the center of the collapsing star.
+Here $H_{h_i}$ is the Hamiltonian constraint
+violation~\eref{eqn:analysis_hamiltonian_constraint} at the center of the
+star for a run with resolution $h_i$.
 Up to the time when the apparent horizon forms, the convergence order is
 $\approx 1.5$ as expected. At later times, the singularity forming at the
 center of the collapsing star renders a pointwise measurement of the