A Scalar Field and the Einstein Vacuum in Modern Kaluza-Klein Theory
  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. 
Paul S. Wesson and James M. Overduin
gr-qc