Effective geometries and generalized uncertainty principle corrections to the Bekenstein-Hawking entropy

TL;DR

This paper constructs black hole geometries incorporating generalized uncertainty principle corrections, revealing a Planck-scale singularity and linking these metrics to nonlinear electrodynamics models, thus extending black hole entropy understanding.

Contribution

It introduces new black hole metrics consistent with GUP corrections and connects them to nonlinear electrodynamics models, preserving the event horizon.

Findings

Existence of a Planck-scale singularity in corrected geometries

Metrics are realizable via nonlinear electrodynamics models

Preservation of the event horizon at the usual position

Abstract

In this work we construct several black hole metrics which are consistent with the generalized uncertainty principle logarithmic correction to the Bekenstein-Hawking entropy formula. After preserving the event horizon at the usual position, a singularity at the Planck scale is found. Finally, these geometries are shown to be realized by certain model of nonlinear electrodynamics, which resembles previously studied regular black hole solutions.