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]