Time Evolution of the Radial Perturbations and Linear Stability of Solitons and Black Holes in a Generalized Skyrme Model

TL;DR

This paper investigates the linear stability and time evolution of radial perturbations in solitons and black holes within a generalized Skyrme model that includes a dilaton, revealing stability properties linked to solution branches and thermodynamic analysis.

Contribution

It provides the first detailed analysis of radial perturbations and stability for solutions in a generalized Skyrme model with a dilaton, extending previous work without scalar fields.

Findings

One solution branch is stable, the other unstable.

Black hole stability aligns with thermodynamic stability from the turning point method.

Existence of two solution branches merging at a critical parameter value.

Abstract

We study the time evolution of the radial perturbation for self-gravitating soliton and black-hole solutions in a generalized Skyrme model in which a dilaton is present. The background solutions were obtained recently by some of the authors. For both the solitons and the black holes two branches of solutions exist which merge at some critical value of the corresponding parameter. The results show that, similar to the case without a scalar field, one of the branches is stable against radial perturbations and the other is unstable. The conclusions for the linear stability of the black holes in the generalized Skyrme model are also in agreement with the results from the thermodynamical stability analysis based on the turning point method.