The Statistical Mechanics of Hawking Radiation

TL;DR

This paper proposes a heuristic statistical mechanics model for Hawking radiation, treating particles as timelike entities and linking microstates to the black hole's surface area, offering new insights into black hole evaporation.

Contribution

It introduces a novel statistical model using a worldline Lagrangian formalism to describe Hawking radiation and microstates, bridging quantum and thermodynamic perspectives.

Findings

Recovered Hawking particle mass from the model

Derived the black hole's thermal energy expression

Quantified microstates based on horizon surface area

Abstract

Hawking radiation and black hole thermodynamics are well understood in the frameworks of quantum field theory and general relativity, with contemporary extensions in string theory, AdS/CFT, and loop quantum gravity. However, an open question remains: Can Hawking radiation be consistently described using statistical mechanics? This challenge arises due to the ambiguous quantum nature of Hawking particles and constraints imposed by information conservation. This study develops a heuristic statistical model using a worldine Lagrangian formalism, treating Hawking particles as timelike with an effective mass and following an arbitrary statistical distribution. The flow of information is modeled as a transfer of microstates from the event horizon to the radiation background within a closed ensemble. From this framework, the Hawking particle mass $m_H=\hbar/(2\pi r_S)$ is recovered, and the worldline Lagrangian yields the black hole's thermal energy, $E=\hbar/(8\pi GM)$. Beyond preserving conventional insights, reinforcing the statistical nature of black hole evaporation, this approach introduces novel perspectives: modeling the black hole as a structured energy well containing microstates, quantifying the evaporation rate of individual microstates, and determining the total number of microstates from the horizon's surface area. This study leaves the door open for a stochastic mechanical analysis, which is introduced in the Discussion section.