Global structure of exact cosmological solutions in the brane world

TL;DR

This paper demonstrates that two recently discovered exact cosmological solutions in brane world models are actually equivalent through an explicit coordinate transformation, clarifying their geometric relationship.

Contribution

It provides an explicit coordinate transformation linking two known solutions, showing they are physically identical, and clarifies the geometric interpretation of one solution.

Findings

Both solutions are exactly the same under a coordinate transformation.

One solution describes a domain wall in 5D Schwarzschild-AdS spacetime.

The region covered by the coordinate system in one solution is clarified.

Abstract

We find the explicit coordinate transformation which links two exact cosmological solutions of the brane world which have been recently discovered. This means that both solutions are exactly the same with each other. One of two solutions is described by the motion of a domain wall in the well-known 5-dimensional Schwarzshild-AdS spacetime. Hence, we can easily understand the region covered by the coordinate used by another solution.