Investigating graviton mass effects on black hole lensing in dRGT massive gravity

Abstract In this paper, we delve into the gravitational lensing and photon trajectories in the vicinity of non-asymptotically flat black hole within the framework of de Rham–Gabadadze–Tolley (dRGT) massive gravity, incorporating a non-zero graviton mass. We assume that both the observer and the light source are located at a finite distance from the lens object, and calculate the gravitational deflection angle of light ray by such a black hole based on Gauss–Bonnet theorem. Furthermore, we analytically derive the angular radius expression of Einstein rings in dRGT massive gravity and briefly discuss the relevant impacts of the graviton mass. Notably, our analytical results suggest potential impacts of the graviton mass on both light deflection angles and Einstein ring characteristics, highlighting its relevance in dRGT massive gravity and expecting the detectability of black holes in gravitational lensing observations.