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