Stability of a vacuum nonsingular black hole

TL;DR

This paper investigates the stability of vacuum nonsingular black holes with de Sitter centers under external perturbations, demonstrating stability for axial perturbations and establishing criteria for polar perturbations.

Contribution

It provides the first detailed stability analysis of vacuum nonsingular black holes with de Sitter cores, including criteria for stability under different perturbation types.

Findings

Objects with de Sitter centers are stable under axial perturbations.

Derived stability criteria for polar perturbations.

Analyzed specific density profiles for stability conditions.

Abstract

This is the first of series of papers in which we investigate stability of the spherically symmetric space-time with de Sitter center. Geometry, asymptotically Schwarzschild for large $r$ and asymptotically de Sitter as $r\to 0$, describes a vacuum nonsingular black hole for $m\geq m_{cr}$ and particle-like self-gravitating structure for $m < m_{cr}$ where a critical value $m_{cr}$ depends on the scale of the symmetry restoration to 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 center to external perturbations. We specify first two types of geometries with and without changes of topology. Then we derive the general equations for an arbitrary density profile and show that in the whole range of the mass parameter $m$ objects described by geometries with de Sitter center remain stable under axial perturbations. In the case of the polar perturbations we find criteria of stability and study in detail the case of the density profile $\rho(r)=\rho_0 e^{-r^3/r_0^2 r_g}$ where $\rho_0$ is the density of de Sitter vacuum at the center, $r_0$ is de Sitter radius and $r_g$ is the Schwarzschild radius.