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Photonspheres, curved hypersurfaces on which massless particles can performclosed geodesic motions around highly compact objects, are an integral part ofgeneric black-hole spacetimes. In the present compact paper we prove, usinganalytical techniques, that the innermost light rings of spherically symmetrichairy black-hole spacetimes whose external matter fields are characterized by atraceless energy-momentum tensor cannot be located arbitrarily close to thecentral black hole. In particular, we reveal the physically interesting factthat the non-linearly coupled Einstein-matter field equations set the lowerbound $r_{\gamma}\geq {6\over5}r_{\text{H}}$ on the radii of tracelessblack-hole photonspheres, where $r_{\text{H}}$ is the radius of the outermostblack-hole horizon.

Lower bound on the radii of light rings in traceless black-hole spacetimes