This question is in reference to the paper here (Equation 3).The extremal 3-brane metic in $D=10$ can be written as:
\begin{equation*}
ds^2 = A^{-1/2}(-dt^2 +dx_1^2 +dx^2+ dx^3) + A^{1/2}(dr^2 +r^2 d\Omega_5^2)
\end{equation*}
where
\begin{equation*}
A = 1+ \frac{R^4}{r^4}
\end{equation*}
In this background the $s$-wave of a minimally coupled massless scalar satisfies:
\begin{equation*}
\left[\rho^{-5}\frac{d}{d\rho}\rho^{5}\frac{d}{d\rho}+ \frac{(\omega R)^{4}}{\rho^{4}}+1\right]\phi(\rho) =0
\end{equation*}
How do I derive this result?

This post imported from StackExchange Physics at 2014-07-28 11:15 (UCT), posted by SE-user Debangshu