Spherically symmetric space-time with the regular de Sitter center

TL;DR

This paper explores a class of globally regular, spherically symmetric solutions to Einstein's equations with a de Sitter core, describing nonsingular black holes, particle-like structures, and cosmological models with evolving vacuum energy.

Contribution

It introduces a new class of regular solutions with a de Sitter center, linking the geometry to variable vacuum energy and analyzing their physical properties.

Findings

Existence of nonsingular black holes and particle-like solutions.

Smooth transition of space-time symmetry from de Sitter to Lorentz.

Models with evolving vacuum energy density and regular cosmological behavior.

Abstract

The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is presented. The source term, invariant under radial boots, is classified as spherically symmetric vacuum with variable density and pressure, associated with an r-dependent cosmological term, whose asymptotic in the origin, dictated by the weak energy condition, is the Einstein cosmological term. For this class of metrics the ADM mass is related to both de Sitter vacuum trapped in the origin and to breaking of space-time symmetry. In the case of the flat asymptotic, space-time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity. Dependently on mass, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole, or G-lump - a vacuum selfgravitating particlelike structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter at both origin and infinity and describes, dependently on parameters and choice of coordinates, a vacuum nonsingular cosmological black hole, selfgravitating particlelike structure at the de Sitter background and regular cosmological models with smoothly evolving vacuum energy density.