Equivalence Between Space-Time-Matter and Brane-World Theories

TL;DR

This paper demonstrates the equivalence between space-time-matter and brane-world theories, showing they predict identical high-energy corrections to general relativity and unify matter with geometry in five dimensions.

Contribution

It establishes the theoretical equivalence between STM and brane-world models, highlighting their shared predictions and conceptual framework.

Findings

STM predicts high-energy corrections identical to brane models

Matter in brane models arises from 5D metric dependence

Proposed combined approach simplifies solution finding in brane theories

Abstract

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.