[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 267)

[diener at cct.lsu.edu]

User: diener
Date: 2012/03/07 11:53 AM

Modified:
 /
  ET.tex

Log:
 Add a citation to Zerilli and explicitly name the Regge-Wheeler and
 Zerilli equations.

File Changes:

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

File [modified]: ET.tex
Delta lines: +5 -3
===================================================================
--- ET.tex	2012-03-07 17:25:31 UTC (rev 266)
+++ ET.tex	2012-03-07 17:53:09 UTC (rev 267)
@@ -1950,8 +1950,9 @@
 on a Schwarzschild background or the calculation of the Weyl scalar $\Psi_4$.
 
 The module \codename{Extract} uses the Moncrief formalism~\cite{
-Moncrief:1974am} to extract gauge-invariant wave functions $Q_{\ell m}^\times$ and $Q_{\ell
-m}^+$ given spherical surfaces of constant coordinate
+Moncrief:1974am} to extract gauge-invariant wave functions $Q_{\ell m}^\times$
+(see~\cite{Regge:1957td}) and $Q_{\ell
+m}^+$ (see~\cite{Zerilli:1970se}) given spherical surfaces of constant coordinate
 radius. The spatial metric is expressed as a perturbation on
 Schwarzschild and expanded into a tensor basis of
 the Regge-Wheeler harmonics~\cite{Regge:1957td} described by six standard
@@ -1969,7 +1970,8 @@
     + \Lambda r K^{+\ell m} \Bigg)
 \end{eqnarray}
 are calculated, where $S=1-2M/r$ and $\Lambda=(\ell-1)(\ell+2)+6M/r$.  
-These functions then satisfy the wave equations:
+These functions then satisfy the Regge-Wheeler ($Q_{\ell m}^\times$) and
+Zerilli ($Q_{\ell m}^+$) wave equations:
 \begin{eqnarray}
    (\partial_t^2-\partial_{r^*}^2)Q_{\ell m}^\times &=& 
       - S \left[ \frac{\ell(\ell+1)}{r^2}-\frac{6M}{r^3} \right]