Photon spheres in Einstein and Einstein-Gauss-Bonnet theories and circular null geodesics in axially-symmetric spacetimes

Abstract

In this article we extend a recent theorem proven by Hod (Phys. Lett. B, {\bf 727}, 345--348, 2013) to $n$-dimensional Einstein and Einstein-Gauss-Bonnet theories, which gives an upper bound for the photon sphere radii of spherically symmetric black holes. As applications of these results we give a universal upper bound for the real part of quasinormal modes in the WKB limit and a universal lower bound for the position of the first relativistic image in the strong lensing regime produced by these type of black holes. For the axially-symmetric case, we also make some general comments (independent of the underlying gravitational theory) on the relation between circular null geodesics and the fastest way to circle a black hole.

In this post-publisher version two typos were corrected: the signature of the metric in eq.(1) and a factor in eq.(102). We thanks Gary Gibbons and Chris Pope for bringing to our attention these typos

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• Light deflection by charged wormholes in Einstein-Maxwell-dilaton theory
• Bounds on Photon Spheres and Shadows of Charged Black Holes in Einstein-Gauss-Bonnet-Maxwell Gravity
• Metamorphoses of a photon sphere
• The extreme orbital period in scalar hairy kerr black holes
• Charged strange star model in Tolman-Kuchowicz spacetime in the background of 5D Einstein-Maxwell-Gauss-Bonnet gravity
• Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity
• The existence of null circular geodesics outside extremal spherically symmetric asymptotically flat hairy black holes
• Upper bound on the radii of regular ultra-compact star photonspheres
• Bound on photon circular orbits in general relativity and beyond
• Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres
• Bounds for Lyapunov exponent of circular light orbits in black holes
• No short hair behaviors of ultra-compact stars
• Light-ring pairs from $A$-discriminantal varieties