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

TL;DR

This paper analyzes gravitational lensing in the Simpson-Visser spacetime across various parameter regimes, revealing unique photon sphere behaviors and divergence patterns of light deflection angles in the strong deflection limit.

Contribution

It provides a comprehensive study of gravitational lensing in Simpson-Visser spacetime for all parameter values, including the novel behavior at the degenerate photon sphere for a=3m.

Findings

Deflection angle diverges nonlogarithmically at the marginally unstable photon sphere.

Multiple photon spheres exist depending on parameters, affecting lensing.

Unique lensing features at the transition points between black holes and wormholes.

Abstract

A Simpson-Visser spacetime has two nonnegative parameters $a$ and $m$ and its metric is correspond with (i) a Schwarzschild metric for $a=0$ and $m\neq0$, (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 $a\neq0$ 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 nonnegative 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.