The Generalized Uncertainty Principle in f(R) Gravity for a Charged Black Hole

TL;DR

This paper derives a charged black hole solution in f(R) gravity using the Palatini formalism, incorporates the generalized uncertainty principle to modify black hole thermodynamics, and analyzes effects on entropy, temperature, and stability for small black holes.

Contribution

It introduces a novel approach to black hole thermodynamics in f(R) gravity with GUP corrections, extending understanding of mini black hole properties.

Findings

Entropy correction to Bekenstein-Hawking formula

Modified temperature and tunneling probability due to GUP

Enhanced stability analysis for small black holes

Abstract

Using f (R) gravity in the Palatini formularism, the metric for a charged spherically symmetric black hole is derived, taking the Ricci scalar curvature to be constant. The generalized uncertainty principle is then used to calculate the temperature of the resulting black hole, through this the entropy is found correcting the Bekenstein-Hawking entropy in this case. Using the entropy the tunneling probability and heat capacity are calculated up to the order of the Planck length, which produces an extra factor that becomes important as black holes become small, such as in the case of mini black holes.