Evolution of nonlinear perturbations inside Einstein-Yang-Mills black holes

Abstract

We present our results on the numerical study of the evolution of nonlinear perturbations inside spherically symmetric black holes in $\mathrm{SU}(2)$ Einstein-Yang-Mills (EYM) theory. Recent developments demonstrate a new type of behavior of the metric for EYM black hole interior; the generic metric exhibits an infinitely oscillating approach to the singularity, which is 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 strong numerical evidence in favor of the nonlinear stability of the generic EYM black hole interior. Alternatively, the EYM black hole interior of Schwarzschild-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.