A Scalar Field and the Einstein Vacuum in Modern Kaluza-Klein Theory

TL;DR

This paper explores a five-dimensional extension of general relativity, deriving a scalar field obeying the Klein-Gordon equation in vacuum with a cosmological constant, and examines implications for massive particles in a universe dominated by vacuum energy.

Contribution

It introduces a simplified gauge in five-dimensional relativity leading to a scalar field governed by the Klein-Gordon equation within Einstein's vacuum equations.

Findings

Scalar field obeys Klein-Gordon equation in vacuum with cosmological constant

Simplified field equations in five-dimensional relativity

Implications for properties of massive particles in vacuum-dominated universe

Abstract

Five-dimensional relativity as an extension of general relativity has field equations that simplify considerably given the adoption of a new gauge. The result is a scalar field governed by the Klein-Gordon equation, in an empty spacetime with a cosmological constant governed by Einstein's equations. The main application is to the properties of massive particles in a vacuum-dominated universe.