Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres

TL;DR

This paper extends Hod's bound on the compactness at the innermost light ring from isotropic to anisotropic horizonless spheres, showing the bound's robustness under anisotropic conditions.

Contribution

It proves that Hod's compactness bound also applies to anisotropic horizonless spheres under similar energy conditions.

Findings

Hod's bound holds for anisotropic spheres

The bound is valid under dominant energy and non-negative trace conditions

Extension from isotropic to anisotropic cases confirmed

Abstract

In the background of isotropic horizonless spheres, Hod recently provided an analytical proof of a bound on the compactness at the innermost light ring with the dominant energy and non-negative trace conditions. In this work, we extend the discussion of isotropic spheres to anisotropic spheres. With the same dominant energy and non-negative trace conditions, we prove that Hod's bound also holds in the case of anisotropic horizonless spheres.