2013/06/30 by R. Casadio, F. Scardigli
Physics and Astronomy · #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1140/epjc/s10052-013-2685-2
8 pages, 5 figures, extended version of arXiv:1305.3195 with new results about the GUP and black hole decay, clarifications about black hole decay added
arxiv created 2013/10/20 · arxiv updated 2015/06/16
A localised 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. In order 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 be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.