User: bmundim Date: 2011/01/24 11:13 AM
Modified: / ET.tex
Log: First draft on the initial data section.
File Changes:
Directory: / ============
File [modified]: ET.tex Delta lines: +63 -2 =================================================================== --- ET.tex 2011-01-24 17:06:57 UTC (rev 11) +++ ET.tex 2011-01-24 17:13:56 UTC (rev 12) @@ -373,8 +373,69 @@
\subsection{Initial Data} -\todo{1/2 page Josh} +\todo{1/2 page Josh, Bruno}
+The Einstein Toolkit contains many thorns used to generate initial data for GR simulations, +including both vacuum and hydrodynamical configurations. These include thorns used primarily +for testing out various components of the evolution scheme as well as physically motivated +configurations that describe single of binary blacks and/or neutron stars. Many of the thorns +are self-contained, consisting of either all the code to generate exact initial solutions or +the numerical tools required to construct solutions known semi-analytically. Others, though, +require the installation of other numerical software packages that are included in the toolkit +as External libraries. The {\tt twopunctures} thorn \cite{Ansorg:2004ds}, commonly used in numerical +relativity to generate binary black hole data, invokes the GNU Scientific Library [GSL; \cite{Galassi:2009}]. +Several thorns have also been implemented to read in datafiles generated by the +{\tt Lorene code} \cite{Loreneweb,GGTMB}, including the BHBH, BHNS, and NSNS data made publicly +available through the Lorene website. + +Scheduling of initial data routines generally follows a standard format. User-defined parameters +are run through a parameter check designed to catch obvious internal inconsistencies, in addition to +any known incompatibilities with other modules of the toolkit. Initial data is then generated +at the proper stage within the Cactus framework, determined primarily by whether the configuration +in question represents vacuum or a hydrodynamical configuration. Finally, any necessary cleanup +is typically performed at the end of the initial step, prior to the iterations forward in time. + +For vacuum initial data configurations, an initial data thorn must supply $g_{ij}$, the spatial 3-metric, +and $K_{ij}$, the extrinsic curvature. While the evolution scheme typically makes use of the BSSN formalism, +the conversion between the physical and conformal metric and extrinsic curvature is handled solely within +evolution thorns, and is not referenced by initial data ones. Optionally, many initial data thorns also +supply values for the lapse and shift vector, and in some cases time derivatives as well, though these +may be supplied by other routines depending on the freedom to choose gauge conditions envisioned for a +specific configuration. + +For hydrodynamic configurations, assuming that an equation of state has been specified, the user must also +supply the values of hydrodynamic variables at all grid locations, in particular the primitive variables +$\rho$, $v_i$ and the energy variable $\epsilon$ for all cases where we don't have a polytype EOS in the +form $P=P(\rho)$ (see Sec.~\ref{???} for a discussion of the use of EOS in the ET). For an MHD configuration, +one must supply all of these along with the initial magnetic field $B^i$ as well. + +The initial data routines currently implemented include the following: +\begin{itemize} +\item Vacuum spacetime tests: +\begin{enumerate} +\item {\tt IDConstraintViolate}: A vacuum spacetime in which the diagonal terms in the spatial metric are +modified by a spatial deformation to explicitly violate the Hamiltonian constraint. +\item {\tt Exact}: A set of exact spacetimes in various coordinates, along with tools to Lorentz boost +those configurations. +\end{enumerate} +\item Vacuum gravitational wave configurations: +\begin{enumerate} +\item {\tt IDBrillData}: A Brill wave spacetime \cite{Brill:1959}. +\item {\tt IDLinearWaves}: A spacetime containing a linear gravitational wave. +\end{enumerate} +\item Black Hole configurations: +\begin{enumerate} +\item {\tt IDAnalyticBH}: This thorn can generate Schwarzchild black holes, as well as the Misner solution +for multiple BHs and the brill-Lindquist binary BH solution. +\item {\tt IDAxibrillBH,~IDAxiOddBrillBH}: These thorns generate single black holes deformed by even and +odd parity axisymmetric perturbations, respectively. +\item {\tt DistortedBHIVP,~RotatingDBHIVP}: These thorns generate single black holes distorted by even +and odd-parity non-axisymmetric perturbation, respectivey. +\item {\tt TwoPunctures}: This thorn generates accurate binary black-hole initial data. +\end{enumerate} +\end{itemize} + + \paragraph{Gravitational Waves}
\paragraph{Black Holes} @@ -424,7 +485,7 @@ \todo{2 pages in total, 1 plot per paragraph, Frank coordinates}
\paragraph{Kerr-Schild} -\todo{1/2 page, who?} +\todo{1/2 page, Bruno} Show stable Kerr-evolution. What is commonly shown for this nowadays, the spectrum of the ringdown of a perturbation?