Fractal Statistics and Quantum Black Hole Entropy

TL;DR

This paper explores how fractal characteristics of quantum paths relate to black hole entropy, deriving its form and explaining the numerical factor through geometric and statistical considerations.

Contribution

It introduces a novel approach linking fractal statistics to quantum black hole entropy, providing a geometric interpretation of its numerical factor.

Findings

Derived the quantum black hole entropy using fractal path considerations

Identified the geometric origin of the entropy's numerical factor

Linked fractal statistics to the counting of geometric quanta

Abstract

Simple considerations about the fractal characteristic of the quantum-mechanical path give us the opportunity to derive the quantum black hole entropy in connection with the concept of fractal statistics. We show the geometrical origin of the numerical factor of four of the quantum black hole entropy expression and the statistics weight appears as a counting of the quanta of geometry.