Gravitational lensing in the Simpson-Visser black-bounce spacetime in a strong deflection limit

Abstract

A Simpson-Visser spacetime has two non-negative parameters $a$ and $m$ and its metric is correspond with (i) a Schwarzschild metric for $a=0$ and $m\ensuremath{\ne}0$, (ii) a regular black hole metric for $a<2m$, (iii) a one-way traversable wormhole metric for $a=2m$, (vi) a two-way traversable wormhole metric for $a>2m$, and (v) an Ellis-Bronnikov wormhole metric for $a\ensuremath{\ne}0$ and $m=0$. The spacetime is one of the most useful spacetimes for the purpose of comprehensively understanding gravitational lensing of light rays reflected by a photon sphere of black holes and wormholes. We have investigated gravitational lensing in the Simpson-Visser spacetime in a strong deflection limit in all the non-negative parameters of $a$ and $m$. In a case of $a=3m$, two photon spheres and an antiphoton sphere at the throat degenerate into a marginally unstable photon sphere. The deflection angle of the light rays reflected by the marginally unstable photon sphere at the throat diverges nonlogarithmically in the strong deflection limit.