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Roberto Casadio, Octavian Micu, Dejan Stojkovic. Horizon Wave-Function and the Quantum Cosmic Censorship. Phys. Lett. B, 2015.

Abstract: We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio a > 1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for a^2 < 2, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for a^2 > 2, and the uncertainty in the location of the horizon blows up at a^2 < 2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value can exist.

Keywords: superextremal black holes, Reissner-Nordström metric, horizon wave function

Posted by Octavian Micu

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