Horizon Wavefunction of Generalized Uncertainty Principle Black Holes

Abstract EN

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 = m 1 + β / 2 M P l 2 / m 2 .

Considering the case of a wave-packet shaped by a Gaussian distribution, we compute the HWF and the probability P B H 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 P B H 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 P B H 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 R H 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 R H ~ M - 1 .