2005/12/01 by V. D. Gladush, Valentin D. Gladush
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #General relativity #Invariant (physics) #Lorentz covariance #Lorentz transformation #Mathematical analysis #Mathematical physics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #gr-qc
paper · pdf · doi:10.1142/s0218271807009851
published as Int.J.Mod.Phys.D16:711-736,2007 · 24 pages, revtex
arxiv created 2005/12/01 · openalex publication_date 2007/04/01 · arxiv updated 2010/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A Lorentz-invariant cosmological model is constructed within the framework of five-dimensional gravity. The five-dimensional theorem which is analogical to the generalized Birkhoff theorem is proved, that corresponds to the Kaluza's "cylinder condition." The five-dimensional vacuum Einstein equations have an integral of motion corresponding to this symmetry, the integral of motion is similar to the mass function in general relativity (GR). Space closure with respect to the extra dimensionality follows from the requirement of the absence of a conical singularity. Thus, the Kaluza–Klein (KK) model is realized dynamically as a Lorentz-invariant mode of five-dimensional general relativity. After the dimensional reduction and conformal mapping the model is reduced to the GR configuration. It contains a scalar field with a vanishing conformally invariant energy–momentum tensor on the flat space–time background. This zero mode can be interpreted as a vacuum configuration in GR. As a result the vacuum-like configuration in GR can be considered as a manifestation of the Lorentz-invariant empty five-dimensional space.