Cosmological term as a source of mass

TL;DR

This paper explores solutions to Einstein's equations with a variable cosmological term that transitions from de Sitter to Minkowski space, describing nonsingular black holes and particlelike structures with implications for quantum vacuum states.

Contribution

It introduces a family of regular, asymptotically flat solutions with an r-dependent cosmological term, unifying black hole and particlelike structures within a single framework.

Findings

Existence of nonsingular black hole solutions with a de Sitter core.

Identification of G-lumps as horizonless, particlelike structures.

Quantum energy spectrum of G-lumps relates to Hawking temperature.

Abstract

In the spherically symmetric case the dominant energy condition together with the requirements of regularity at the center, asymptotic flatness and fineteness of the ADM mass, defines the family of asymptotically flat globally regular solutions to the Einstein minimally coupled equations which includes the class of metrics asymptotically de Sitter at approaching the regular center. The source term corresponds to an r-dependent cosmological term given by the second rank symmetric tensor invariant under boosts in the radial direction and evolving from de Sitter vacuum in the origin to Minkowski vacuum at infinity. Space-time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through the radial boosts in between. The standard formula for the ADM mass relates it to the de Sitter vacuum replacing a central singularity at the scale of symmetry restoration. For masses exceeding a certain critical value m_{crit} de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole, while beyond m_{crit} it describes a G-lump which is a vacuum selfgravitating particlelike structure without horizons. Quantum energy spectrum of G-lump is shifted down by the binding energy, and zero-point vacuum mode is fixed at the value corresponding to the Hawking temperature from the de Sitter horizon.