Black Holes, Space-Filling Chains and Random Walks

TL;DR

This paper explores how black hole radii in various dimensions can be modeled as random walks, proposing a microscopic chain-based explanation for these structures within black holes.

Contribution

It introduces a novel microscopic chain model to explain the random walk behavior of black hole radii across different dimensions.

Findings

Black hole radius relates to Brownian and fractional Brownian walks.

A microscopic chain filling the black hole interior explains the random walk structure.

Provides a unified view of black hole entropy and geometry.

Abstract

Many approaches to a semiclassical description of gravity lead to an integer black hole entropy. In four dimensions this implies that the Schwarzschild radius obeys a formula which describes the distance covered by a Brownian random walk. For the higher-dimensional Schwarzschild-Tangherlini black hole, its radius relates similarly to a fractional Brownian walk. We propose a possible microscopic explanation for these random walk structures based on microscopic chains which fill the interior of the black hole.