Black Hole Thermodynamics from a Noncommutative Area Operator

TL;DR

This paper introduces a noncommutative area operator to calculate black hole thermodynamics, deriving key properties like temperature and entropy using quantum statistical methods.

Contribution

It presents a novel approach by incorporating a noncommutative two-dimensional area spectrum into black hole thermodynamics calculations.

Findings

Derived the partition function for a black hole with noncommutative area spectrum

Calculated temperature and entropy of Schwarzschild black holes using this framework

Analyzed the evaporation time based on the new thermodynamical properties

Abstract

One key element to calculate thermodynamical properties for a black hole is the partition function. In this paper we have incorporated the idea of a two dimensional area in a noncommutative space and were able to calculate the partition function with such a spectra. Employing the canonical quantum statistics formalism we compute the temperature, entropy and time of evaporation for a Schwarzschild black hole.