The physical properties of Kaluza--Klein solitons

Abstract

We take the interpretation of Kaluza--Klein theory where curvature in 4+1 dimensions induces effective matter in 3+1 dimensions, and calculate the physical properties of solitons. These are exact solutions of the 5D equations that are static and have spherical symmetry in ordinary (3D) space. We find that their effective 4D matter properties obey the equation of state of ultra-relativistic particles or radiation, and that the matter is highly concentrated towards the centre. The choice of parameters that gives back the conventional Schwarzschild solution is somewhat anomalous, but we gain new insight into this solution. For the general class of solitons, the conventionally defined gravitational mass goes to zero at the centre. However, that point is a singularity where the 4+1 and 3+1 scalars defined by the geometry diverge. We conclude that Kaluza--Klein solitons are naked singularities in ordinary space, surrounded by highly compressed clouds of hot matter that are analogous to point sources in Einstein theory.