Black Hole Entropy and the Modified Uncertainty Principle: A heuristic analysis

TL;DR

This paper investigates quantum corrections to black hole entropy using a generalized uncertainty principle with a linear momentum term, finding consistent leading order corrections and extending results to black holes with multiple horizons.

Contribution

It introduces a heuristic method to compute quantum corrected black hole entropy based on a modified uncertainty principle, applicable to both single and multi-horizon spacetimes.

Findings

Leading order correction proportional to the square root of horizon area.

Negative logarithmic correction matches previous results.

Method valid for black holes with inner and outer horizons.

Abstract

Recently Ali et.al.(2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea here we calculate the quantum corrected value of a Schwarzschild black hole entropy and a Reissner-Nordstrom black hole with double horizon by utilizing the proposed generalized uncertainty principle. We find that the leading order correction goes with the square root of the horizon area contributing positively. We also find that the prefactor of the logarithmic contribution is negative and the value exactly matches with some earlier existing calculations. With the Reissner-Nordstrom black hole we see that this model independent procedure is not only valid for single horizon spacetime but also valid for spacetimes with inner and outer horizons.