Photon regions, shadow observables, and constraints from M87* of a charged rotating black hole

Inspired by the observations of the supermassive black hole M87* by the Event Horizon Telescope (EHT), a remarkable surge in black hole physics is to use the black hole shadow's observables to distinguish between general relativity and modified theories of gravity, which could also help to reveal the astrophysical nature of the central black hole in the EHT observation. In this paper, we study a charged rotating black hole in conformal gravity, in which the term related to the charge has different falloffs from the usual Kerr-Newman (KN) black hole. We investigate the spacetime properties including the horizons, ergospheres, and photon regions; then, we show the boundary of the black hole shadow and investigate its characteristic observables. These features closely depend on the spin and charge parameters, which are compared with those in Kerr and KN black holes. Then, presupposing that M87* is a charged rotating black hole in conformal gravity, we constrain the black hole parameters via the observational constraints from EHT. We find that the constraints on the inferred circularity deviation (0. 1) and shadow axial ratio (1<Dₗ4/3) for M87* are satisfied for the entire parameter space of the charged rotating black hole in conformal gravity. However, the shadow angular diameter ₃=423 gives an upper bound on the parameter space. Our findings indicate that the current charged rotating black hole in conformal gravity could be a candidate for astrophysical black holes. Moreover, the EHT observation of the axial ratio Dₗ may help us to distinguish between a Kerr black hole and the current charged rotating black hole in conformal gravity in some parameter space.