Boltzmann factor and Hawking radiation

TL;DR

This paper demonstrates that corrections to Hawking radiation spectra can be derived directly from fundamental thermodynamics and statistical mechanics principles, specifically through modifications of the Boltzmann factor.

Contribution

It shows that the known corrections to Hawking radiation spectra naturally follow from basic thermodynamic and statistical mechanics principles, unifying previous results.

Findings

Corrections to Hawking radiation spectrum follow from thermodynamics.

Boltzmann factor modifications lead to spectrum corrections.

Provides a fundamental basis for known spectrum corrections.

Abstract

Hawking radiation has thermal spectrum corresponding to the temperature ${T}_{H}={(8{\pi}M)}^{-1}$, where $M$ is the mass (energy) of the black hole. Corrections to the Hawking radiation spectrum were discovered by Kraus and Wilczek (1995) and Parikh and Wilczek (2000). Here I show that these corrections follow directly from the basic principles of thermodynamics and statistical mechanics. In essence, it is the Boltzmann factor that ought to be corrected; corrections to the Hawking (or any other) radiation spectrum then follow necessarily.