User: diener Date: 2012/03/05 02:01 PM

Modified: / ET.tex

Log: Added the Christodoulou formula (with reference) and slightly changed the notation.

File Changes:

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

File [modified]: ET.tex Delta lines: +13 -2 =================================================================== --- ET.tex 2012-03-05 18:40:12 UTC (rev 254) +++ ET.tex 2012-03-05 20:01:40 UTC (rev 255) @@ -1866,8 +1866,10 @@ There are also the quasi-local measures of mass and angular momentum, from any \ahz{s} found during the spacetime. Both \codename{AHFinderDirect} and \codename{AHFinder} output the -corresponding irreducible mass derived from the area of the horizon $m_H = -\sqrt{A/(16\pi)}$. +corresponding irreducible mass derived from the area of the horizon +$M_{\mathrm{ir}} = +\sqrt{A/(16\pi)}$. Note that the irreducible mass is smaller than the total +mass if the black hole is spinning.

The module \codename{QuasiLocalMeasures} implements the calculation of mass and spin multipoles from the isolated @@ -1885,6 +1887,15 @@ can calculate useful quantities such as the Weyl or Ricci scalars or the three-volume element of the horizon world tube in addition to physical observables such as mass and momenta. +For the calculation of the total mass \codename{QuasiLocalMeasures} uses the +Christodoulou mass~\cite{Christodoulou:1970wf} +\begin{equation} + M^2 = M_{\mathrm{ir}}^2+\frac{S^2}{4 M_{\mathrm{ir}}^2}, +\label{eq:christodoulou} +\end{equation} +that takes into account the +contributions of the irreducuble mass $M_{\mathrm{ir}}$ and angular +momemtum $S$ to the total black hole mass $M$.

Finally, the module \codename{HydroAnalysis} additionally locates the (coordinate) center of mass as well as the point of maximum rest mass density of a