Evolution of Nonlinear Perturbations Inside Einstein-Yang-Mills Black Holes

TL;DR

This paper numerically investigates the nonlinear evolution of perturbations inside Einstein-Yang-Mills black holes, revealing a generic oscillatory approach to singularity and demonstrating the stability of typical black hole interiors.

Contribution

It provides the first detailed numerical analysis of nonlinear perturbations inside EYM black holes, showing stability of generic interiors and instability of special S-type solutions.

Findings

Generic EYM black hole interiors exhibit oscillatory approach to singularity.

Generic interiors are nonlinearly stable under perturbations.

S-type interiors are unstable and evolve into generic type.

Abstract

We present our results on numerical study of evolution of nonlinear perturbations inside spherically symmetric black holes in the SU(2) Einstein-Yang-Mills (EYM) theory. Recent developments demonstrate a new type of the behavior of the metric for EYM black hole interiors; the generic metric exhibits an infinitely oscillating approach to the singularity, which is a spacelike but not of the mixmaster type. The evolution of various types of spherically symmetric perturbations, propagating from the internal vicinity of the external horizon towards the singularity is investigated in a self-consistent way using an adaptive numerical algorithm. The obtained results give a strong numerical evidence in favor of nonlinear stability of the generic EYM black hole interiors. Alternatively, the EYM black hole interiors of S(chwarzschild)-type, which form only a zero measure subset in the space of all internal solutions are found to be unstable and transform to the generic type as perturbations are developed.