Lower bound on the compactness of isotropic ultra-compact objects

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.

5 pages

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• Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres
• Trapping of null geodesics in slowly rotating spacetimes
• No short hair behaviors of ultra-compact stars