From vacuum nonsingular black hole to variable cosmological constant

TL;DR

This paper presents a class of regular, spherically symmetric solutions in general relativity that transition smoothly from de Sitter to Schwarzschild geometries, describing nonsingular black holes evolving into horizonless, particle-like structures, and extends to variable cosmological constants.

Contribution

It introduces a new class of solutions connecting de Sitter and Schwarzschild spacetimes with a smooth source term, including variable cosmological constants, and describes their physical implications.

Findings

Describes nonsingular black holes evolving into G-lumps.

Extends solutions to variable cosmological constants.

Links ADM mass to de Sitter vacuum properties.

Abstract

We outline the class of globally regular spherically symmetric solutions to the minimally coupled GR equations asymptotically de Sitter in the origin and asymptotically Schwarzschild at infinity. A source term connects smoothly de Sitter vacuum at the regular center with Minkowski vacuum at infinity and corresponds to anisotropic spherically symmetric vacuum defined macroscopically by the algebraic structure of its stress-energy tensor invariant under boosts in the radial direction. De Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole which evolves, in the course of Hawking evaporation, towards a self-gravitating particle-like structure without horizons, G-lump. Space-time symmetry changes smoothly from the de Sitter group in the center to the Lorentz group at infinity, and the standard formula for the ADM mass relates it to the de Sitter vacuum replacing a singularity at the scale of symmetry restoration. This class of metrics is easily extended to the case of a nonzero background cosmological constant. A source term connects then smoothly two de Sitter vacua with different values of cosmological constant which makes possible to associate anisotropic spherically symmetric vacuum with an r-dependent cosmological term.