Linearized Five Dimensional Kaluza-Klein Theory as a Gauge Theory

TL;DR

This paper develops a linearized five-dimensional Kaluza-Klein theory as a gauge theory, unifying linearized gravity and Maxwell's electromagnetism, with potential applications in gravitational wave polarization analysis.

Contribution

It introduces a gauge-theoretic formulation of linearized Kaluza-Klein gravity in five dimensions, connecting gravity and electromagnetism, and explores applications in gravitational wave polarization.

Findings

Unified linearized gravity and Maxwell equations in 5D

Applicable to flat and De Sitter backgrounds

Potential use in gravitational wave polarization analysis

Abstract

We develop a linearized five dimensional Kaluza-Klein theory as a gauge theory. By perturbing the metric around flat and the De Sitter backgrounds, we first discuss linearized gravity as a gauge theory in any dimension. In the particular case of five dimensions, we show that using the Kaluza-Klein mechanism, the field equations of our approach implies both linearized gauge gravity and Maxwell theory in flat and the De Sitter scenarios. As a possible further development of our formalism, we also discuss an application in the context of a gravitational polarization scattering by means of the analogue of the Mueller matrix in optical polarization algebra. We argue that this application can be of particular interest in gravitational waves experiments.