Homogeneous space-times as models for isolated extended objects

Abstract

An extended object is considered on the Minkowski background in the form of a space-time bag, which is bounded by a certain surface confining an internal substance. An internal metric is built starting from the symmetry principles rather than from the field equations. Assuming such a surface to be Lorentz invariant we find that the internal space is proved to be the de Sitter space. Conformal inversion of the internal metric relative to the bag surface determines an external space (conformally conjugated de Sitter space) whose metric may simulate a field of the object. Although the extended object built in a such a way is noncompact, its cross section by the hyperplane r^0=0, where r^0 is the temporal coordinate, is compact (a ball) and the associated metric can model a spherically symmetric extended massless charge in a certain approximation.