Kaluza-Klein Gravity

TL;DR

This review assesses higher-dimensional gravity through a general-relativistic lens, contrasting compactified, projective, and noncompactified Kaluza–Klein approaches. It shows how 5D geometry can reproduce 4D gravity and electromagnetism, how extra dimensions can be compactified or conceptually reinterpreted, and how noncompactified models permit induced matter and novel cosmological/astrophysical predictions. The work surveys exact solutions, cosmological dynamics, solitons, and classical tests, highlighting that none of the three pathways is yet ruled out by observations, while stressing the need for further tests and clearer physical interpretation of the fifth dimension. Overall, the KK framework provides a rich, testable arena for exploring gravity, matter, and gauge interactions beyond standard 4D GR. The findings underscore potential links to dark matter candidates, cosmological dynamics, and precision tests of gravity, with significant implications for future experiments and theoretical development.

Abstract

We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identified and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time.