# S-Wave for minimally coupled scalar field

+ 1 like - 0 dislike
141 views

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
Quick guess, haven't tried it: 1. Work out the Klein-Gordon equation for $\phi$ using the standard expressions for the curved space Laplacian. 2. Make an s-wave ansatz. 3. Simplify.
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOve$\varnothing$flowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.