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authorallen <allen@6a3ddf76-46e1-4315-99d9-bc56cac1ef84>2002-05-09 11:50:57 +0000
committerallen <allen@6a3ddf76-46e1-4315-99d9-bc56cac1ef84>2002-05-09 11:50:57 +0000
commitc26c84861a4cb282162aca3b2b1678f87622dc35 (patch)
treede697cc9ceb3e4dacf7ff751be0b13c8036cc6bb
parentb64c391c54f53cbca366dbdbaa993d39304e00d5 (diff)
changed to Einstein2
git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinInitialData/IDAnalyticBH/trunk@115 6a3ddf76-46e1-4315-99d9-bc56cac1ef84
-rw-r--r--doc/documentation.tex70
1 files changed, 35 insertions, 35 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex
index deafab2..5493b0b 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -62,7 +62,7 @@ initial dataset for black hole evolution that can be specified
analytically in terms of the metric, $g_{ab}$, and extrinsic
curvature, $K_{ab}$.
-The thorn extends the \texttt{einstein::initial\_data} parameter by
+The thorn extends the \texttt{admbase::initial\_data} parameter by
adding the following datasets:
\begin{description}
\item[\texttt{schwarzschild}] Schwarzschild, in isotropic
@@ -75,10 +75,10 @@ Initial data for lapse and shift can also be specified in
this thorn.\\
The Cactus grid-functions corresponding to the initial data are
-inherited from the thorn \texttt{CactusEinstein/Einstein}, along with
-the conformal factor grid-function, \texttt{psi}, and its derivatives
-which are optionally set based on the value of the parameter
-\texttt{einstein::use\_conformal}.\\
+inherited from the thorn \texttt{CactusEinstein/ADMBase}, along with
+the conformal factor grid-function, \texttt{psi} from \texttt{CactusEinstein/StaticConformal}, and its derivatives
+which are optionally set based on the value of the parameters
+\texttt{admbase::metric\_type} and \texttt{staticconformal::conformal\_storage}.\\
The \texttt{IDAnalyticBH} has been written and augmented over an number of
years by many Cactus authors. These include John Baker, Steve Brandt,
@@ -90,7 +90,7 @@ associated parameters in turn.
The Schwarzschild metric corresponds to a single, static, black hole.
If the Cactus metric is specified as a conformal metric (by setting
-\texttt{einstein::use\_conformal="yes"}), then the metric is
+\texttt{admbase::metric\_type="yes"}), then the metric is
set using isotropic coordinates \cite{mtw-isotropic}:
\begin{equation}
ds^2 = -\left(\frac{2r - M}{2r + M}\right)^2
@@ -109,19 +109,19 @@ The mass is specified using the parameter
\texttt{idanalyticbh::mass}. The black hole is assumed to reside at
the origin of the grid, corresponding to the location $x=y=z=0$.\\
-If the \texttt{einstein::use\_conformal} parameter has been set, then
-the metric grid-functions (\texttt{einstein::gxx}, $\ldots$,
-\texttt{einstein::gzz}) are given as $\delta_{ab}$, and the conformal
-factor \texttt{einstein::psi} is set to the value specified
+If the \texttt{admbase::metric\_type} parameter has been set to {\tt static conformal}, then
+the metric grid-functions (\texttt{admbase::gxx}, $\ldots$,
+\texttt{admbase::gzz}) are given as $\delta_{ab}$, and the conformal
+factor \texttt{staticconformal::psi} is set to the value specified
above. The derivatives of the conformal factor
-(\texttt{einstein::psix}, etc.) are determined analytically.
+(\texttt{staticconformal::psix}, etc.) are determined analytically.
In order to give the lapse an initial profile which corresponds to
isotropic lapse of the $4$-metric specified above, use the parameter
\begin{verbatim}
idanalyticbh::initial_lapse = "schwarz"
\end{verbatim}
-This will cause the \texttt{einstein::alp} grid-function to be
+This will cause the \texttt{admbase::alp} grid-function to be
initialised to the value:
\begin{equation}
\alpha = \frac{2r - M}{2r + M}.
@@ -129,9 +129,9 @@ initialised to the value:
Note that the Schwarzschild data has the following non-standard
-behaviour in response to the \texttt{einstein::use\_conformal}
+behaviour in response to the \texttt{admbase::metric\_type}
parameter. If the \emph{physical} metric is requested
-(ie. \texttt{use\_conformal} is set to \texttt{"no"}) then a
+(ie. \texttt{metric\_type} is set to \texttt{"physical"}) then a
\emph{different} form of the Schwarzschild metric is set:
Schwarzschild coordinates are set instead of the isotropic
coordinates:
@@ -145,12 +145,12 @@ black hole of mass $m=1$, using an initial lapse of $\alpha=1$, you
could modify your parameter file as follows:
\begin{verbatim}
- ActiveThorns = "... Einstein IDAnalyticBH ..."
+ ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..."
- einstein::use_conformal = "yes"
+ admbase::metric_type = "static conformal"
- einstein::initial_data = "schwarzschild"
- einstein::initial_lapse = "one" # or "schwarz" for isotropic lapse
+ admbase::initial_data = "schwarzschild"
+ admbase::initial_lapse = "one" # or "schwarz" for isotropic lapse
idanalyticbh::mass = 1.0
\end{verbatim}
@@ -179,13 +179,13 @@ respectively. \emph{(Note that the default values for these parameters
are $M=2$ and $a=0.1$.)} The black hole is assumed to reside at the
centre of the coordinate system, at $x=y=z=0$.
-The \texttt{einstein::use\_conformal} parameter can be used to specify
+The \texttt{admbase::metric\_type} parameter can be used to specify
whether the metric should be conformal or not. If the metric is
conformal, then $\psi$ is initialised as a separate grid function, and
it's first and second derivatives are calculated analytically and also
stored as grid functions. Otherwise, the conformal factor is
multiplied through in the expression for the 3-metric before the
-values of the \texttt{einstein::metric} variables are set. The
+values of the \texttt{admbase::metric} variables are set. The
extrinsic curvature is also determined analytically.
The gauge can be set to the Kerr lapse and shift with the parameters
@@ -206,13 +206,13 @@ where
A set of parameters which initialise an evolution to use the Kerr
intial data with mass $M=1$ and angular momentum $a=0.3$ are:
\begin{verbatim}
- ActiveThorns = "... Einstein IDAnalyticBH ..."
+ ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..."
- einstein::use_conformal = "yes"
+ admbase::metric_type = "static conformal"
- einstein::initial_data = "kerr"
- einstein::initial_lapse = "kerr"
- einstein::initial_shift = "kerr"
+ admbase::initial_data = "kerr"
+ admbase::initial_lapse = "kerr"
+ admbase::initial_shift = "kerr"
idanalyticbh::mass = 1.0
idanalyticbh::a_kerr = 0.3
@@ -283,18 +283,18 @@ This quantity is determined automatically and written to standard
output.
If the conformal form of the metric is used (via the
-\texttt{einstein::use\_conformal} parameter), then derivatives of the
+\texttt{admbase::metric\_type} parameter), then derivatives of the
conformal factor are computed analytically from the derivatives of the
above expression for $\psi$.
To make use of the two black hole initial data, a variation of the
following set of parameters can be used:
\begin{verbatim}
- ActiveThorns = "... Einstein IDAnalyticBH ..."
+ ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..."
- einstein::use_conformal = "yes"
+ admbase::metric_type = "static conformal"
- einstein::initial_data = "misner_bh"
+ admbase::initial_data = "misner_bh"
idanalyticbh::mu = 2.2
\end{verbatim}
@@ -337,11 +337,11 @@ stencil is hardcoded at $dx=10^-6$.
As an example, a parameter file implementing 3 Misner black holes on a
circle of radius $\cosh 4$ would use the following parameters:
\begin{verbatim}
- ActiveThorns = "... Einstein IDAnalyticBH ..."
+ ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..."
- einstein::use_conformal = "yes"
+ admbase::metric_type = "static conformal"
- einstein::initial_data = "multiple_misner_bh"
+ admbase::initial_data = "multiple_misner_bh"
idanalyticbh::misner_nbh = 3
idanalyticbh::mu = 4
@@ -389,11 +389,11 @@ To initialise a run with a pair of Brill-Lindquist black holes with
masses $1$ and $2$ and located at $\pm 1$ on the $y$-axis, a set of
parameters such as the following could be used:
\begin{verbatim}
- ActiveThorns = "... Einstein IDAnalyticBH ..."
+ ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..."
- einstein::use_conformal = "yes"
+ admbase::metric_type = "static conformal"
- einstein::initial_data = "bl_bh"
+ admbase::initial_data = "bl_bh"
idanalyticbh::bl_nbh = 2