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

Abstract

Abstract Photonspheres, curved hypersurfaces on which massless particles can perform closed geodesic motions around highly compact objects, are an integral part of generic black-hole spacetimes. In the present compact paper we prove, using analytical techniques, that the innermost light rings of spherically symmetric hairy black-hole spacetimes whose external matter fields are characterized by a traceless energy-momentum tensor cannot be located arbitrarily close to the central black hole. In particular, we reveal the physically interesting fact that the non-linearly coupled Einstein-matter field equations set the lower bound $$ {r}_{\gamma}\ge \frac{6}{5}{r}_H $$ r γ ≥ 6 5 r H on the radii of traceless black-hole photonspheres, where rH is the radius of the outermost black-hole horizon.