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In the background of isotropic horizonless spheres, Hod recently provided ananalytical proof of a bound on the compactness at the innermost light ring withthe dominant energy and non-negative trace conditions. In this work, we extendthe discussion of isotropic spheres to anisotropic spheres. With the samedominant energy and non-negative trace conditions, we prove that Hod's boundalso holds in the case of anisotropic horizonless spheres.

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