An Investigation of Equivalence between Bulk-based and Brane-based Approaches

TL;DR

This paper explores the theoretical equivalence between bulk-based and brane-based approaches in brane-world models, demonstrating how a general anisotropic bulk metric can produce a brane-based metric in Gaussian Normal Coordinates.

Contribution

It provides a formalism showing the conditions under which bulk-based and brane-based approaches are equivalent in brane-world models, extending previous specific model results.

Findings

Bulk-based metrics can produce brane-based metrics in Gaussian Normal Coordinates.

The formalism preserves spatial anisotropy between approaches.

Equivalence is demonstrated for a general anisotropic bulk metric.

Abstract

There are two different approaches to handle brane-world models brane-based or bulk-based. In the brane-based approach, the brane is chosen to be fixed on a coordinate system, whereas in the bulk-based approach, it is no longer static as it moves along the extra dimension. It is aimed to get a general formalism of the equivalence between two approaches obtained for a specific model in Mukohyama et all [12]. We found that calculations driven by a general anisotropic bulk-based metric yields a brane-based metric in Gaussian Normal Coordinates by conserving spatial anisotropy.