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

TL;DR

This paper extends bounds on photon sphere radii in higher-dimensional Einstein and Einstein-Gauss-Bonnet black holes, linking these bounds to quasinormal modes and gravitational lensing, and discusses null geodesics in axially-symmetric spacetimes.

Contribution

It generalizes a recent theorem to higher dimensions and modified gravity theories, providing universal bounds relevant for black hole physics and observational signatures.

Findings

Upper bounds for photon sphere radii in higher-dimensional black holes.

Universal bounds for quasinormal mode frequencies.

Insights into null geodesics and gravitational lensing 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.