diff options
Diffstat (limited to 'doc/documentation.tex')
| -rw-r--r-- | doc/documentation.tex | 60 |
1 files changed, 55 insertions, 5 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex index 95e145d..e2116cb 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -1298,20 +1298,32 @@ This is controlled by the following parameters: \begin{description} \item[%%% \begin{tabular}{@{}l@{}} - \code{run\_at\_CCTK\_ANALYSIS} \\ - \code{run\_at\_CCTK\_POSTSTEP} \\ - \code{run\_at\_CCTK\_POSTINITIAL} %%%\\ + \code{run\_at\_CCTK\_ANALYSIS} \\ + \code{run\_at\_CCTK\_POSTSTEP} \\ + \code{run\_at\_CCTK\_POSTINITIAL} \\ + \code{run\_at\_CCTK\_POST\_RECOVER\_VARIABLES} %%%\\ \end{tabular} ] \mbox{}\\ These parameters (which default to \verb|true|, \verb|false|, - and \verb|false| respectively) control which schedule bins - \thorn{AHFinderDirect} runs in. Historically, + \verb|false|, and \verb|true| respectively) control which + schedule bins \thorn{AHFinderDirect} runs in. Historically, \thorn{AHFinderDirect} ran in CCTK\_ANALYSIS, and that's still the default, but these parameters allow you to change this so it runs in CCTK\_POSTSTEP and/or CCTK\_POSTINITIAL instead. (You can even run in all three bins if you want!) + In general we need to run at CCTK\_POST\_RECOVER\_VARIABLES, since + \begin{itemize} + \item parameters may have been steered at recovery, so we may need + to find a new horizon or horizons, and + \item we need to set the mask again to make sure it's correct + right away (since our next regular horizon-finding may not + be until some time steps later) + \end{itemize} + Therefore the \verb|run_at_CCTK_POST_RECOVER_VARIABLES| parameter + should probably be left at its default setting of \verb|true|. + \item[%%% \begin{tabular}{@{}l@{}} \code{geometry\_interpolator\_name} \\ @@ -1651,6 +1663,44 @@ AHFinderDirect::initial_guess__coord_sphere__radius[1] = 2.0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Surfaces of Constant Expansion} + +Surfaces of Constant Expansion (CE surfaces) are introduced in +\cite{AHFinderDirect/Schnetter03a} as a generalisation of +apparent horizons (AH). On an AH surface, the expansion is zero +everywhere. On a CE surfaces, the expansion is still everywhere the +same, but it need not be zero. CE surfaces are also a generalisation +of Constant Mean Curvature surfaces (CMC surfaces); both are identical +when the extrinsic curvature vanishes. As described in +\cite{AHFinderDirect/Schnetter03a}, it is likely that CE +surfaces foliate the spacelike hypersurface outside of some interior +region. This interior region is inside the common apparent horizon, +if it exists. + +CE surfaces can give some insight into the spacetime, because they can +be used to analyse the part of the spacelike hypersurface ``between +the horizons and infinity''. Most notably, they can be used to look +at the region where a common horizon is about to (or believed to) +form. Similarly, one can use them for collapsing stars where an +apparent horizon has not yet formed. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Pretracking} + +Apparent horizon pretracking is introduced in +\cite{AHFinderDirect/Schnetter03a}. This is an application +of CE surfaces. Even when there is no common horizon, there are still +common CE surfaces surrounding multiple black holes. Pretracking +consists of tracking in time the smallest common CE surface that can +be found. It is reasonable to believe that this surface will evolve +into the common horizon at the time where this common horizon begins +to exist. The expansion of this smallest CE surface is also an +indication of how close the spacelike hypersurface is to having a +common apparent horizon. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{How \thorn{AHFinderDirect} Works} \label{AHFinderDirect/sect-how-ahfinderdirect-works} |