Stability of a vacuum non-singular black hole

Abstract

This is the first of series of papers in which we investigate stability of the spherically symmetric spacetime with de Sitter centre. Geometry, asymptotically Schwarzschild for large r and asymptotically de Sitter as r → 0, describes a vacuum non-singular black hole for m ⩾ mcr and particle-like self-gravitating structure for m < mcr where a critical value mcr depends on the scale of the symmetry restoration to the de Sitter group in the origin. In this paper, we address the question of stability of a vacuum non-singular black hole with de Sitter centre to external perturbations. We specify first two types of geometries with and without changes of topology. Then we derive the general equations governing polar perturbations, specify criteria of stability for a regular black hole with de Sitter centre, and study in detail the case of the density profile where ρ0 is the density of de Sitter vacuum at the centre, is the de Sitter radius and rg is the Schwarzschild radius.