Abstract
We argue that the variational method in Wald type thought experiments, involves order of magnitude problems when one imposes the fact that delta M is inherently a first order quantity itself. One observes that the contribution of the second order perturbations is actually of the fourth order. Therefore backreactions have to be explicitly calculated. Here, we re-consider the overspinning problem for Kerr–Newman black holes interacting with test fields. We calculate the backreaction effects due to the induced increase in the angular velocity of the event horizon, which brings a partial solution to the overspinning problem. To bring an ultimate solution, we argue that the absorption probability should be taken into account in Wald type problems where black holes interact with test fields. This fundamentally alters the course of the analysis of the thought experiments. Due to the fact that a small fraction of the challenging modes is absorbed by the black holes, overspinning is prevented for both nearly extremal and extremal cases. Some extreme cases are easily fixed by backreaction effects. The arguments do not apply to the generic overspinning by fermionic fields for which the absorption probability is positive definite.
Highlights
One of the main unsolved problems in classical general relativity is the validity of the cosmic censorship conjecture due to Penrose [1]
In a very recent work we showed that the absorption of the test fields that could overspin nearly extremal black holes is not allowed due to the increase in the angular velocity of the event horizon before the absorption of the field [9]
We have argued that the increase in the angular velocity of the horizon leads to an increase in the superradiance limit, which will prevent the absorption of the challenging modes for a class of nearly extremal Kerr–Newman black holes with α 0.5
Summary
One of the main unsolved problems in classical general relativity is the validity of the cosmic censorship conjecture due to Penrose [1]. Hubeny adapted an alternative approach to Wald type problems where one starts with a nearly extremal black hole instead of an extremal one [4] She showed that a nearly extremal Reissner–Nordström black hole can be overcharged into a naked singularity by a test body. Düztasand Semiz derived the same result for nearly extremal Kerr black holes interacting with test fields [6] In these works the overspinning and overcharging of nearly extremal black holes are not quite generic, which suggests that they should be fixed by employing backreaction effects. In a very recent work we showed that the absorption of the test fields that could overspin nearly extremal black holes is not allowed due to the increase in the angular velocity of the event horizon before the absorption of the field [9]. The possibility to destroy the event horizon in the asymptotically anti-de Sitter cases has become
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