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Extremal black hole formation as a critical phenomenon
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In this paper, we prove that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal black hole. Physically, these solutions can be understood as beams of gravitationally self-interacting collisionless charged particles fired into Minkowski space from past infinity. Depending on the precise value of the parameter, we show that the Vlasov matter either disperses due to the combined effects of angular momentum and electromagnetic repulsion, or undergoes gravitational collapse. At the critical value of the parameter, an extremal Reissner-Nordstr\"om black hole is formed. No naked singularities occur as the extremal threshold is crossed. We call this critical phenomenon extremal critical collapse and the present work constitutes the first rigorous result on the black hole formation threshold in general relativity.
Forward citations
Cited by 6 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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Violation of the third law of black hole mechanics in vacuum gravity
Numerical gluing constructions show finite-time formation of an extremal Myers-Perry black hole in five-dimensional vacuum gravity, from Schwarzschild or from no black hole.
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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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Thermodynamics of Black Holes, far from Equilibrium
The paper derives finite, physical-process versions of the first and second laws of black hole thermodynamics for dynamical horizon segments, extending the first law to black holes arbitrarily far from equilibrium.
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Formation of extremal Reissner-Nordstr\"om black holes: insights from numerics
For several scalar-field profiles, extremal Reissner-Nordström black holes can be glued from collapse only above a profile-dependent threshold in eM, and only for scalar masses below about m/e≈0.28.
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On the third law of black hole mechanics for supersymmetric black holes
Supersymmetric black holes cannot form in finite time from matter obeying the local mass-charge inequality, and a non-extremal black hole cannot evolve into a supersymmetric one in finite time.
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