Horizon Wavefunction of Generalized Uncertainty Principle Black Holes

Luciano Manfredi,Jonas Mureika

doi:10.1155/2016/1543741

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 m is replaced by M=m1+β/2MPl2/m2. Considering the case of a wave-packet shaped by a Gaussian distribution, we compute the HWF and the probability PBH that the source is a (quantum) black hole, that is, that it lies within its horizon radius. The case β<0 is qualitatively similar to the standard Schwarzschild case, and the general shape of PBH 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 β and drops to 0 for a minimum mass value. The scenario differs significantly for increasing β>0, where a minimum in PBH is encountered, thus meaning that every particle has some probability of decaying to a black hole. Furthermore, for sufficiently large β we find that every particle is a quantum black hole, in agreement with the intuitive effect of increasing β, which creates larger M and RH 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 (1+1) dimensions and the horizon size grows as RH~M-1.

Highlights

Black holes are special objects in gravitational physics because they are expected to reveal features of both classical and quantum gravitation
Inspired by the dual role of m in the Generalized Uncertainty Principle (GUP), we explore the existence of sub-Planckian black holes, that is, quantum mechanical objects that are simultaneously elementary particles and black holes
Considering the case of a wave-packet shaped by a Gaussian distribution, the corresponding Horizon Wavefunction was computed and the probability PBH that the source is a black hole, that is, that it lies within its horizon radius, was calculated

Summary

Introduction

Black holes are special objects in gravitational physics because they are expected to reveal features of both classical and quantum gravitation. Large black holes may reveal hints of quantum effects through, for example, the morphology of their shadows [1], it is anticipated that eventual observation of quantum scale black holes formed in high-energy collisions will provide direct evidence In this regime, these objects transcend classical and quantum gravitation, and forming reliable predictions of their physics becomes tenuous in the absence of a complete theory of quantum gravity. After first reviewing the formalism for both HWF and the GUP metric in Sections 2 and 3, we derive expressions for the HWF and black hole probabilities in both the super- and sub-Planckian mass regimes for varying GUP model parameters In the former case, we find the results to be in agreement with those of the Schwarzschild HWF.

The Horizon Wavefunction Formalism

Generalized Uncertainty Principle Black Holes

HWF of GUP Black Holes

Conclusions