Horizon Wave-Function and the Quantum Cosmic Censorship

TL;DR

This paper uses the horizon wave-function formalism to explore quantum effects on the Cosmic Censorship Conjecture, suggesting a quantum limit on the charge-to-mass ratio for black holes beyond which they cannot be well-defined.

Contribution

It extends the horizon wave-function approach to charged particles, proposing a quantum limit on charge-to-mass ratio for black hole formation.

Findings

Normalisable horizon wave-function for charge-to-mass ratio squared less than 2

Probability of black hole formation remains non-zero in this regime

Horizon uncertainty diverges at charge-to-mass ratio squared equal to 2

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 $\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\alpha^2<{2}$, 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 $\alpha^2 > 2$, and the uncertainty in the location of the horizon blows up at $\alpha^2=2$, 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 (of the order of $\sqrt{2}$) can exist.