Black hole production in the presence of a maximal momentum in horizon wave function formalism

Abstract

We study the Horizon Wave Function (HWF) description of a generalized uncertainty principle (GUP) black hole in the presence of two natural cutoffs as a minimal length and a maximal momentum. This is motivated by a metric which allows the existence of sub-Planckian black holes, where the black hole mass [Formula: see text] is replaced by [Formula: see text]. Considering a wave-packet with a Gaussian profile, we evaluate the HWF and the probability that the source might be a (quantum) black hole. By decreasing the free parameter, the general form of probability distribution, [Formula: see text], is preserved, but this resulted in reducing the probability for the particle to be a black hole accordingly. The probability for the particle to be a black hole grows when the mass is increasing slowly for larger positive [Formula: see text], and for a minimum mass value it reaches to [Formula: see text]. In effect, for larger [Formula: see text] the magnitude of [Formula: see text] and [Formula: see text] increases, matching with our intuition that either the particle ought to be more localized or more massive to be a black hole. The scenario undergoes a change for some values of [Formula: see text] significantly, where there is a minimum in [Formula: see text], so this expresses that every particle can have some probability of decaying to a black hole. In addition, for sufficiently large [Formula: see text], we find that every particle could be fundamentally a quantum black hole.