Probing a regular non-minimal Einstein-Yang-Mills black hole with gravitational lensings

Abstract

We investigate weak and strong deflection gravitational lensings of the regular black hole predicted by a non-minimal Einstein–Yang–Mills theory. We find that its weak deflection lensing is the same as a Reissner–Nordström black hole's. Observables in the strong deflection lensing, including the apparent radius of the photon sphere (shadow) as well as the angular separation, brightness difference and time delay between relativistic images, are obtained and analyzed for the supermassive black holes Sgr A* and M87* in the Galactic Center and at the center of M87. We find that only the apparent radii of the photon spheres are within the ability of current technology, whereas there is not enough resolution to distinguish the regular Einstein–Yang–Mills black hole from the Reissner–Nordström one. Meanwhile, caution needs to be paid when the diameter of M87*'s shadow measured by the Event Horizon Telescope is directly taken to constrain such a regular black hole. Keywords: Non-minimal Einstein–Yang–Mills theory, Regular black hole, Gravitational lensing