Horizon wave-function and the quantum cosmic censorship

Roberto Casadio,Octavian Micu,Dejan Stojkovic

doi:10.1016/j.physletb.2015.05.053

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 superextremal case (with charge-to-mass ratio α>1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α2<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 α2>2, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2) can exist.

Highlights

A complete understanding of the gravitational collapse of a compact object remains one of the most challenging issues in contemporary theoretical physics
We find that one can still obtain a normalisable horizon wave-function (HWF) for α2 < 2, and this configuration has a non-vanishing probability of being a black hole, extending the classically allowed region for a charged black hole
The literature on the subject has grown immensely, many technical and conceptual issues remain. One of these is the famous Cosmic Censorship Conjecture (CCC), proposed by Penrose in 1969 [3], which states that no singularities will ever become visible to an outer observer in a generic gravitational collapse starting from reasonable nonsingular initial states

Summary

Introduction

A complete understanding of the gravitational collapse of a compact object remains one of the most challenging issues in contemporary theoretical physics. The Horizon Wave Function (HWF) formalism was proposed [6], as a way of quantising the Einstein equation that determines the gravitational radius of a spherically symmetric matter source and its time evolution [7], which instead relates the quantum state of the horizon to the quantum state of matter This formalism was applied to a few different case studies [8,9,10], yielding apparently sensible results in agreement with (semi)classical expectations, and there is hope that it will facilitate our understanding of the formation of BHs from QM particles.

Electrically charged spherical sources

HWF for Gaussian sources

Superextremal geometry

Conclusions