Gravitational lensing by black holes with multiple photon spheres

We study gravitational lensing of light by hairy black holes, which, in a certain parameter regime, can possess two photon spheres of different size outside the event horizon. In particular, we focus on higher -order images of a pointlike light source and a luminous celestial sphere produced by strong gravitational lensing near photon spheres. Two photon spheres usually triple the number of high-order images of a pointlike light source. When a hairy black hole is illuminated by a celestial sphere, two photon spheres would give rise to two critical curves in the black hole image, and the smaller critical curve coincides with the shadow edge. In addition to a set of higher-order images of the celestial sphere outside the shadow edge, two more sets of higher-order images are observed inside and outside the larger critical curve, respectively.

Automated summary

This study focuses on gravitational lensing of light by hairy black holes, specifically the higher-order images produced near photon spheres. It is found that two photon spheres can triple the number of high-order images of a pointlike light source, with two critical curves appearing in the black hole image. Additionally, multiple sets of higher-order images are observed inside and outside the larger critical curve.