Eur. Phys. J. C (2018) 78: 208
https://doi.org/10.1140/epjc/s10052-018-5715-2

Regular Article - Theoretical Physics

Horizon quantum fuzziness for non-singular black holes

¹ Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, Munich, Germany
² Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40126, Bologna, Italy
³ I.N.F.N., Sezione di Bologna, IS-FLAG, Via B. Pichat 6/2, 40127, Bologna, Italy

^* e-mail: A.Giugno@physik.uni-muenchen.de

Received: 10 January 2018
Accepted: 5 March 2018
Published online: 13 March 2018

Abstract

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein’s field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.