An exotic class of Kaluza-Klein models

TL;DR

This paper introduces a novel class of Kaluza-Klein models where the extra dimensions are non-compact and particles are gravitationally confined near a four-dimensional subspace, challenging traditional compactification assumptions.

Contribution

It presents a specific five-dimensional model demonstrating gravitational trapping of particles without compact internal spaces, expanding the scope of Kaluza-Klein theories.

Findings

Particles can be gravitationally trapped near a 4D submanifold in non-compact extra dimensions

The model exhibits confinement without the need for compact internal spaces

Revived interest in non-compact extra dimensions in modern theoretical physics

Abstract

We discuss an exotic class of Kaluza-Klein models in which the internal space is neither compact nor even of finite volume. Rather than using the usual compact internal space we consider the case where particles are gravitationally trapped near a four-dimensional submanifold of the higher dimensional spacetime. A specific model exhibiting this phenomenon is constructed in five dimensions. Physics Letters B159, 22-25 (1985). Note: This rather old paper has recently been subject of renewed interest due to the explosion of activity in the ``non-compact extra dimensions'' variant of the Kaluza-Klein model. It is not available elsewhere on the Internet, and in the interests of easy access I am placing it on hep-th. The body of the paper is identical to the published version. A small separate note has been added at the end of the paper.