Uncertainty Principles and Non-local Black Holes

TL;DR

The paper investigates whether non-local gravity in Infinite Derivative Gravity (IDG) can be recast as effective Generalized and Extended Uncertainty Principles (GUP/EUP) in the context of black holes. By matching UV and IR non-local gravitational corrections to GUP- and EUP-inspired black-hole metrics, it derives constraints on the GUP parameter $\beta$ and the EUP parameter $\alpha$ in terms of the non-local scales $L_{UV}$ and $L_*$ and the black-hole mass $m$, predicting universal deviations from GR such as reduced event horizons ($R_{EH} \ll R_S$) and higher evaporation temperatures ($T_e \gg T_H$). Specifically, UV matching yields $\beta \approx -24.1\,G m^2 \approx -\dfrac{m^2}{M_P^2}$, leading to $R_{EH} \approx 0.5\,R_S$ and $T_e \approx 2\,T_H$, while IR matching gives $\alpha \approx -0.2\,\dfrac{L_*^2}{G^2 m^2}$, yielding $R_{EH} \approx 0.1\,R_S$ and $T_e \approx 10\,T_H$. The results suggest GUP/EUP are effective low-energy descriptions of fundamentally non-local gravity and point to potential quantum-level equivalence-principle violations, with implications for astrophysical and cosmological tests of non-locality.

Abstract

We discuss the Generalized Uncertainty Principle and the Extended Uncertainty Principle in the context of black hole solutions coming from non-local theories of gravity, focusing, specifically, on Infinite Derivative Gravity. We argue that these modifications of the Heisenberg Uncertainty Principle are effective descriptions arising from the non-local features of gravitational interaction. By comparing the predictions of both the modified uncertainty principles and non-local gravity, we find theoretical constraints on otherwise free parameters as well as universal laws for black hole physics beyond General Relativity.