Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit

TL;DR

This paper derives a formula for the deflection angle of light near a marginally unstable photon sphere in various spacetimes, revealing a nonlogarithmic divergence, and applies it to specific black hole models.

Contribution

It introduces a new analytical expression for the deflection angle in strong gravity regimes near marginally unstable photon spheres.

Findings

Deflection angle diverges nonlogarithmically at the marginally unstable photon sphere.

The formula is successfully applied to Reissner-Nordstrom and Hayward spacetimes.

Provides insights into gravitational lensing near black holes with unstable photon spheres.

Abstract

We investigate the deflection angle in a strong deflection limit for a marginally unstable photon sphere in a general asymptotically flat, static and spherically symmetric spacetime under some assumptions to calculate observables. The deflection angle of a light ray reflected by the marginally unstable photon sphere diverges nonlogarithmically while the one reflected by a photon sphere diverges logarithmically. We apply our formula to a Reissner-Nordstrom spacetime and Hayward spacetime.