Black hole motion in Euclidean space as a diffusion process

TL;DR

This paper derives a diffusion equation for black hole motion in Euclidean space, linking quantum area quantization and entropy to a diffusion process, providing a novel perspective on black hole thermodynamics.

Contribution

It introduces a diffusion-based model for black hole dynamics derived from Bunster-Carlip equations, connecting quantum area quantization and entropy.

Findings

Solution is a Gaussian distribution

Second moment relates to quantum of area

Entropy matches Bekenstein-Hawking entropy with corrections

Abstract

A diffusion equation for a black hole is derived from the Bunster-Carlip equations. Its solution has the standard form of a Gaussian distribution. The second moment of the distribution determines the quantum of black hole area. The entropy of diffusion process is the same, apart from the logarithmic corrections, as the Bekenstein-Hawking entropy.