# Randall-Sundrum metric

1. Jul 20, 2007

### touqra

The Randall-Sundrum metric for extra dimension is the following:

$$ds^2 = e^{-2ky}g_{ab}dx^adx^b - dy^2$$

What is causing this warping or strange metric? I mean a space without force should be totally flat like what we deal with in SR, so there must be something that is causing this warping.

2. Jul 20, 2007

### Haelfix

Thats a good question, and you really have to go back to their original papers for the full details (its semi inspired from String theory where say branes seperated by a distance k are interacting). But the full computation of the exact metric from the field equations is afaik, fairly involved.

From classical reasoning though, its the same thing as warping in the vicinity of any massive object (eg say a cosmic string), eg the redshift at one end of (picture a compactified cylinder naively) the throat (or Brane) is quite naturally a different scale than the other end, this *warps* spacetime and crumples up that finite dimension, as you can see from that exponential factor in the metric.

(edit: Not that involved actually, because they ansatz the solution... see
http://arxiv.org/PS_cache/hep-ph/pdf/9905/9905221v1.pdf)

Last edited: Jul 20, 2007
3. Jul 20, 2007

### touqra

In the paper above, there's this term called KK excitation. What does it mean? If it means excitation like the n-excitation states of a particle in a quantum well, then, I don't really understand how it is calculated in this metric...