User: tbode Date: 2011/01/30 04:54 PM

Modified: / ET.tex

Log: Analysis section draft.

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

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\subsection{Analysis} -\todo{1/2 page Tanja} +%\todo{1/2 page Tanja}

-\paragraph{Masses} +Any simulated system may have many applicable quantities for analysis which +are most efficiently calculated during evolution. The Einstein Toolkit +currently includes modules to facilitate the calculation of the most common +analysis quantities: masses, horizons, and gravitational waves. In addition +to these, detailed below, the \codename{ADMConstraints} module calculates the +constraints required, but not imposed by, the formulation for assessing the +simulation's accuracy and stability. Finally, \codename{ADMAnalysis} calculates +several quantities often needed in analyzing the spacetime evolution: the trace +of the extrinsic curvature $K$, the determinant of the 3-metric, the spatial +metric and extrinsic curvature in spherical coordinates, and the spatial Ricci +tensor and trace.

-\paragraph{Event and Apparent Horizons} +\subsubsection*{Horizons} For spacetimes which contain a \bh{,} the Toolkit +contains modules to find both the event and apparent horizons and their +properties. The \codename{EHFinder} module traces null surfaces backwards in +time through a pre-evolved spacetime. The Toolkit also includes two separate +apparent horizon finders: Thornburg's \codename{AHFinderDirect} and +\codename{AHFinder}.

-\paragraph{Gravitational Waves} +\subsubsection*{Masses} In analyzing spacetimes, it is important to calculate +the masses and momenta of the system. Several Toolkit modules include the +capability of calculating several types of masses. The apparent horizon modules +include in their output the areal masses of the found horizons. The +\codename{Extract} module calculates ADM mass and momenta when extracting +gravitational waves. Additionally, \codename{HydroAnalysis} calculates finds +the center of mass and the point of maximum matter density of a hydronamic +field.

+\subsubsection*{Gravitational Waves} Within the Toolkit are modules for extracting +gravitational waves using two formulations: the Moncrief formalism assuming +the spacetime approximates spherical symmetry \codename{Extract}) and the Weyl +scalar $\Psi_4$ constructed on a fiducial tetrad (\codename{WeylScal4}). The +Weyl scalars, as well as any other quantity, can be projected onto a basis +of spin-weighted spherical harmonics using the \codename{Multipole} module.

\subsection{Relativity Tools} \todo{1/2 page Peter}