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Advances in High Energy Physics
Volume 2016 (2016), Article ID 1543741, 8 pages
http://dx.doi.org/10.1155/2016/1543741
Research Article

Horizon Wavefunction of Generalized Uncertainty Principle Black Holes

Department of Physics, Loyola Marymount University, Los Angeles, CA 90045-2659, USA

Received 27 September 2016; Revised 14 November 2016; Accepted 17 November 2016

Academic Editor: Elias C. Vagenas

Copyright © 2016 Luciano Manfredi and Jonas Mureika. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We study the Horizon Wavefunction (HWF) description of a Generalized Uncertainty Principle inspired metric that admits sub-Planckian black holes, where the black hole mass is replaced by . Considering the case of a wave-packet shaped by a Gaussian distribution, we compute the HWF and the probability that the source is a (quantum) black hole, that is, that it lies within its horizon radius. The case is qualitatively similar to the standard Schwarzschild case, and the general shape of is maintained when decreasing the free parameter but shifted to reduce the probability for the particle to be a black hole accordingly. The probability grows with increasing mass slowly for more negative and drops to 0 for a minimum mass value. The scenario differs significantly for increasing , where a minimum in is encountered, thus meaning that every particle has some probability of decaying to a black hole. Furthermore, for sufficiently large we find that every particle is a quantum black hole, in agreement with the intuitive effect of increasing , which creates larger and terms. This is likely due to a “dimensional reduction” feature of the model, where the black hole characteristics for sub-Planckian black holes mimic those in dimensions and the horizon size grows as .