Simple observations concerning black holes and probability

TL;DR

This paper explores the analogy between black hole properties and probability theory limit distributions, proposing that the central limit theorem may underpin black hole statistical mechanics and the emergent nature of gravity.

Contribution

It introduces a novel analogy linking black hole entropy and information content to stable limit distributions in probability theory, suggesting a fundamental role for the central limit theorem.

Findings

Black holes share properties with stable limit distributions.

Entropy maximization and holographic bounds have analogues in probability theory.

The central limit theorem may be fundamental to black hole thermodynamics.

Abstract

It is argued that black holes and the limit distributions of probability theory share several properties when their entropy and information content are compared. In particular the no-hair theorem, the entropy maximization and holographic bound, and the quantization of entropy of black holes have their respective analogues for stable limit distributions. This observation suggests that the central limit theorem can play a fundamental role in black hole statistical mechanics and in a possibly emergent nature of gravity.