A model displaying extremely inhomogeneous matter distribution in General Relativity

TL;DR

This paper introduces a recursive hierarchical model in General Relativity that results in highly inhomogeneous matter distribution, yet exhibits a slowly converging average density without fractal characteristics.

Contribution

It presents a novel recursive hierarchical metric model demonstrating inhomogeneous matter distribution with unexpected average density behavior.

Findings

Matter distribution is extremely inhomogeneous.

Average mass density tends to a constant very slowly.

No fractal dimension is observed in the distribution.

Abstract

We consider a toy metric in four dimensional space-time defined in terms of a recursive hierarchical prescription. The matter distribution turns out to be extremely inhomogeneous. Surprisingly, for very large samples the average mass density tends (very slowly) to a constant. There is no trace of fractal dimension left.