https://doi.org/10.1140/epjc/s10052-013-2685-2
Regular Article - Theoretical Physics
Horizon wave function for single localized particles: GUP and quantum black-hole decay
1
Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126, Bologna, Italy
2
I.N.F.N., Sezione di Bologna, viale Berti Pichat 6/2, 40127, Bologna, Italy
3
Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy
4
Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan
* e-mail: roberto.casadio@bo.infn.it
Received:
20
October
2013
Accepted:
2
December
2013
Published online:
24
January
2014
A localized particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle’s energy density exceeds a certain threshold, it should be a black hole. To combine these two pictures, we introduce a horizon wave function determined by the particle wave function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass may be a black hole. We also show that our construction entails an effective generalized uncertainty principle (GUP), simply obtained by adding the uncertainties coming from the two wave functions associated with a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.
© The Author(s), 2014
