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What happens at the horizon(s) of an extreme black hole?
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A massless scalar field exhibits an instability at the event horizon of an extreme black hole. We study numerically the nonlinear evolution of this instability for spherically symmetric perturbations of an extreme Reissner-Nordstrom (RN) black hole. We find that generically the endpoint of the instability is a non-extreme RN solution. However, there exist fine-tuned initial perturbations for which the instability never decays. In this case, the perturbed spacetime describes a time-dependent extreme black hole. Such solutions settle down to extreme RN outside, but not on, the event horizon. The event horizon remains smooth but certain observers who cross it at late time experience large gradients there. Our results indicate that these dynamical extreme black holes admit a C^1 extension across an inner (Cauchy) horizon.
Forward citations
Cited by 3 Pith papers
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A Nonlinear Endpoint of Charged Horizon Instabilities
Charged scalar collapse can form dynamical extremal black holes whose horizons show divergent energy density and constant charge hair, with universal near-threshold scaling.
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Taming the Aretakis instability: extremal black holes with multi-degenerate horizons
Black holes with infinitely degenerate horizons are proposed to be stable against Aretakis instability, potentially serving as end states.
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Approaching a dynamical extreme black hole horizon
Explicit JT-gravity solutions give closed-form descriptions of the late-time approach to dynamical extreme Reissner-Nordström black holes with persistent Aretakis instability.
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