Lower bound on the compactness of isotropic ultra-compact objects

TL;DR

This paper establishes a fundamental lower bound on the compactness of isotropic ultra-compact objects with light rings, advancing understanding of their physical limits and properties.

Contribution

It provides the first analytical proof of a lower bound on the compactness of isotropic ultra-compact objects with light rings.

Findings

Ultra-compact isotropic objects must have a compactness parameter greater than 7/12.

The result applies to horizonless spacetimes with light rings.

Analytical techniques were used to derive the bound.

Abstract

Horizonless spacetimes describing spatially regular ultra-compact objects which, like black-hole spacetimes, possess closed null circular geodesics (light rings) have recently attracted much attention from physicists and mathematicians. In the present paper we raise the following physically intriguing question: How compact is an ultra-compact object? Using analytical techniques, we prove that ultra-compact isotropic matter configurations with light rings are characterized by the dimensionless lower bound $\text{max}_r\{2m(r)/r\}>7/12$ on their global compactness parameter.