On the Nature of Inner Light-Rings

Non-singular horizonless ultracompact objects provide a simple resolution tothe black holes singularity problem. It has been shown that, if these objectsare compact enough to exhibit the presence of the light-ring required to mimicthe phenomenology of general relativity black holes, they must have at leastone additional light-ring. The stability of the inner light ring has beenproven under the assumption of Einstein equations and the validity of the nullenergy condition. Since this can have important repercussions on theinstability of a horizonless ultracompact object and the existence of thelatter requires some modified gravitational dynamics and/or exotic matter, itis desirable to obtain a model-independent proof of the stability of theadditional light-ring. In this paper, we prove the stability of the innerlight-ring without any assumption on the dynamics of the theory, while assumingthat the outer light-ring has the same properties as the Kerr light-ring. Giventhe stringent observational constraints on the geometry at the outer light-ringscale, our result now rests solely on geometric considerations and applies toany theory of gravity with any matter content that cannot be ruled out byobservations.