THE PHYSICAL-PROPERTIES OF KALUZA-KLEIN SOLITONS

We take the interpretation of Kaluza-Klein theory where curvature in 4 + 1 dimensions induces effective matter in 3 + 1 dimensions, and calc ulate the physical properties of solitons. These are exact solutions o f the 5D equations that are static and have spherical symmetry in ordi nary (3D) space. We find that their effective 4D matter properties obe y the equation of state of ultra-relativistic particles or radiation, and that the matter is highly concentrated towards the centre. The cho ice of parameters that gives back the conventional Schwarzschild solut ion is somewhat anomalous, but we gain new insight into this solution. For the general class of solitons, the conventionally defined gravita tional mass goes to zero at the centre. However, that point is a singu larity where the 4 + 1 and 3 + 1 scalars defined by the geometry diver ge. We conclude that Kaluza-Klein solitons are naked singularities in ordinary space, surrounded by highly compressed clouds of hot matter t hat are analogous to point sources in Einstein theory.