Connection between two forms of extra-dimensional metrics revisited

TL;DR

This paper explores two different coordinate descriptions of a 5D cosmological model with a 3-brane, establishing a transformation between static and time-dependent metrics to better understand their relationship.

Contribution

It provides an explicit coordinate transformation linking static and time-dependent metrics in a 5D brane-world cosmological model.

Findings

Derived the transformation between static and dynamic coordinate systems.

Clarified the geometric relationship between two metric descriptions.

Enhanced understanding of brane dynamics in higher-dimensional models.

Abstract

5D cosmological model with 3-brane with matter is considered. The brane divides bulk in two AdS half spaces. Geometry of the model can be described by two types of coordinates: in the first setting the metric is static and the brane is moving in the bulk, in the second approach the metric is time-dependent and the brane is located at a fixed position in the bulk. Coordinate transformation connecting two coordinate systems is constructed.