Cosmological term, mass, and space-time symmetry

TL;DR

This paper explores regular, asymptotically flat solutions to Einstein's equations with a cosmological term, revealing connections between de Sitter vacuum, black holes, and particle-like structures, with implications for fundamental particle sizes and unification scales.

Contribution

It introduces a class of globally regular solutions linking de Sitter and Minkowski vacua, and applies these to estimate particle sizes and unification scales.

Findings

Existence of regular solutions with de Sitter core and Minkowski exterior.

Application of solutions to estimate fundamental particle sizes.

Evaluation of gravito-electroweak unification scale from neutrino data.

Abstract

In the spherically symmetric case the requirements of regularity of density and pressures and finiteness of the ADM mass $m$, together with the weak energy condition, define the family of asymptotically flat globally regular solutions to the Einstein minimally coupled equations which includes the class of metrics asymptotically de Sitter as $r\to 0$. A source term connects smoothly de Sitter vacuum in the origin with the Minkowski vacuum at infinity and corresponds to anisotropic vacuum defined macroscopically by the algebraic structure of its stress-energy tensor invariant under boosts in the radial direction. Dependently on parameters, geometry describes vacuum nonsingular black holes, and self-gravitating particle-like structures whose ADM mass is related to both de Sitter vacuum trapped in the origin and smooth breaking of space-time symmetry. The geometry with the regular de Sitter center has been applied to estimate geometrical limits on sizes of fundamental particles, and to evaluate the gravito-electroweak unification scale from the measured mass-squared differences for neutrino.