Generalized uncertainty principles, effective Newton constant and regular black holes

TL;DR

This paper investigates how generalized uncertainty principles influence quantum gravity, leading to an effective Newton constant that models regular black holes and their tunneling processes, suggesting a remnant state as the final outcome.

Contribution

It introduces a novel connection between generalized uncertainty principles and an effective Newton constant, enabling regular black hole models and analysis of tunneling probabilities with quantum corrections.

Findings

Effective Newton constant inspired by GUP influences black hole regularization.

Minimal black hole models are derived from the simplest GUP.

Black hole tunneling probability is regularized by remnant size.

Abstract

In this paper, we explore the quantum spacetimes that are potentially connected with the generalized uncertainty principles. By analyzing the gravity-induced quantum interference pattern and the Gedanken for weighting photon, we find that the generalized uncertainty principles inspire the effective Newton constant as same as our previous proposal. A characteristic momentum associated with the tidal effect is suggested, which incorporates the quantum effect with the geometric nature of gravity. When the simplest generalized uncertainty principle is considered, the minimal model of the regular black holes is reproduced by the effective Newton constant. The black hole's tunneling probability, accurate to the second order correction, is carefully analyzed. We find that the tunneling probability is regularized by the size of the black hole remnant. Moreover, the black hole remnant is the final state of a tunneling process that the probability is minimized. A theory of modified gravity is suggested, by substituting the effective Newton constant into the Hilbert-Einstein action.