[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 257)

[diener at cct.lsu.edu]

User: diener
Date: 2012/03/05 02:31 PM

Modified:
 /
  ET.tex

Log:
 Make the equation defining the irreducible mass a displayed equation so
 I can refer to it later.

File Changes:

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

File [modified]: ET.tex
Delta lines: +8 -4
===================================================================
--- ET.tex	2012-03-05 20:09:52 UTC (rev 256)
+++ ET.tex	2012-03-05 20:31:26 UTC (rev 257)
@@ -1866,9 +1866,12 @@
 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 
-$M_{\mathrm{ir}} = 
-\sqrt{A/(16\pi)}$. Note that the irreducible mass is smaller than the total
+corresponding irreducible mass $M_{\mathrm{ir}}$ derived from the area of the horizon 
+\begin{equation}
+M_{\mathrm{ir}} = 
+\sqrt{\frac{A}{16\pi}}. \label{eq:irreducible}
+\end{equation}
+Note that $M_{\mathrm{ir}}$ is smaller than the total
 mass if the black hole is spinning.
 
 The module \codename{QuasiLocalMeasures} implements
@@ -2321,7 +2324,8 @@
 
 Since there is non-trivial gravitational wave content in the initial data,
 the mass of the BH changes during its evolution. In figure~\ref{fig:ah_mass},
-we show in the top plot the irreducible mass as calculated by
+we show in the top plot the irreducible mass (see 
+equation~(\ref{eq:irreducible})) as calculated by
 \codename{AHFinderDirect} as a function of time at the high (black solid curve),
 medium (blue dashed curve) and low (red dotted curve) resolutions.
 \begin{figure}