Homogeneous space-times as models for isolated extended objects

TL;DR

This paper models extended objects as space-time bags with internal de Sitter geometry, using symmetry principles to derive their metrics, and explores their potential to simulate fields of extended masses or charges.

Contribution

It introduces a novel approach to modeling extended objects via internal de Sitter space derived from symmetry, without relying on field equations.

Findings

Internal space is de Sitter space due to Lorentz invariance.

Conformal inversion relates internal and external metrics, modeling object fields.

Cross section of the object is a compact ball, useful for modeling extended charges.

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.