Formation and decay of Einstein-Yang-Mills black holes

Abstract

We study various aspects of black holes and gravitational collapse in Einstein-Yang-Mills theory under the assumption of spherical symmetry. Numerical evolution on hyperboloidal surfaces extending to future null infinity is used. We begin by constructing colored and Reissner-Nordström black holes on surfaces of constant mean curvature and analyze their perturbations. These linearly perturbed black holes are then evolved into the nonlinear regime and the masses of the final Schwarzschild black holes are computed as a function of the initial horizon radius. We compare with an information-theoretic bound on the lifetime of unstable hairy black holes derived by Hod. Finally we study critical phenomena in gravitational collapse at the threshold between different Yang-Mills vacuum states of the final Schwarzschild black holes, where the n ¼ 1 colored black hole forms the critical solution. The work of Choptuik et al. [Phys. Rev. D 60, 124011 (1999)] is extended by using a family of initial data that includes another region in parameter space where the colored black hole with the opposite sign of the Yang-Mills potential forms the critical solution. We investigate the boundary between the two regions and discover that the Reissner-Nordström solution appears as a new approximate codimension-two attractor.

Stability of gravitating charged-scalar solitons in a cavity

“…However, both the solitons and hairy black holes were soon found to be unstable [11][12][13][14][15][16][17]. Under perturbation, the black holes lose their gauge-field hair and evolve towards a (stable) vacuum black hole solution; the solitons either collapse to form a vacuum black hole or else the gauge field is radiated away to infinity, leaving pure Minkowski spacetime [18][19][20]. This prompts an intriguing question: are there scenarios in which the converse occurs, i.e., in which a vacuum black hole spontaneously evolves towards a hairy configuration which is stable?…”

Numerical evidence for universality in the excited instability spectrum of magnetically charged Reissner–Nordström black holes

“…2 In particular, this interesting numerical study [13] has explicitly demonstrated that, during a near-critical evolution of the Yang-Mills field, the time spent in the vicinity of an unstable SU(2) Reissner-Nordström black-hole solution is characterized by the critical scaling law 3…”

“…The recent numerical work of Rinne [13] has revealed that these unstable SU(2) Reissner-Nordström black-hole spacea e-mail: shaharhod@gmail.com times play the role of approximate 1 codimension-two intermediate attractors (that is, nonlinear critical solutions [14]) in the dynamical gravitational collapse of the Yang-Mills field. 2 In particular, this interesting numerical study [13] has explicitly demonstrated that, during a near-critical evolution of the Yang-Mills field, the time spent in the vicinity of an unstable SU(2) Reissner-Nordström black-hole solution is characterized by the critical scaling law 3…”

“…Indeed, Rinne [13] has recently computed numerically the characteristic unstable eigenvalues of these magnetically charged black-hole solutions of the Einstein-Yang-Mills theory. 4 In the present paper we shall analyze these numerically computed black-hole eigenvalues in an attempt to identify a possible hidden pattern which characterizes the black-hole instability spectrum.…”

“…Interestingly, the critical exponents of the scaling law (1) are directly related to the characteristic instability eigenvalues of the corresponding SU(2) Reissner-Nordström black holes [13]:…”