Kaluza-Klein Reduction of a Quadratic Curvature Model

TL;DR

This paper applies the Palatini variational principle to a five-dimensional quadratic curvature gravity model, deriving four-dimensional field equations that unify gravity, electromagnetism, and a scalar dilaton field through Kaluza-Klein reduction.

Contribution

It introduces a novel quadratic curvature gravity model in five dimensions and demonstrates its reduction to four dimensions, naturally incorporating Lorentz force and unifying fundamental interactions.

Findings

Lorentz force emerges naturally from the reduced equations

Kaluza-Klein equations are intrinsically contained in the model

Unified description of gravity, electromagnetism, and scalar field

Abstract

Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza-Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor in four dimensional spacetime are obtained. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force naturally emerges from the reduced field equations and the equations of the standard Kaluza-Klein theory is demonstrated to be intrinsically contained in this model.