Fifth force from fifth dimension: a comparison between two different approaches

TL;DR

This paper explores how an extra dimension can induce a fifth force in spacetime, comparing two different theoretical approaches through specific geometric models.

Contribution

It introduces and compares two approaches to modeling the fifth force in higher-dimensional gravity theories using explicit geometric examples.

Findings

Both approaches successfully describe the fifth force effects.

The Ricci-flat warped-product and Randall-Sundrum models illustrate differences in the approaches.

The study clarifies the role of extra dimensions in gravitational dynamics.

Abstract

We investigate the dynamics of particles moving in a spacetime augmented by one extra dimension in the context of the induced matter theory of gravity. We examine the appearance of a fifth force as an effect caused by the extra dimension and discuss two different approaches to the fifth force formalism. We then give two examples of application of both approaches by considering the case of a Ricci-flat warped-product manifold and a generalized Randall-Sundrum space.