The masses and shadows of the black holes Sagittarius A* and M87* in modified gravity (MOG)

We present calculations for the anticipated shadow sizes of Sgr A* and the supermassive black hole in the galaxy M87 in the context of the MOG modified theory of gravity (also known as Scalar-Tensor-Vector-Gravity, or STVG). We demonstrate that mass estimates derived from stellar and gas dynamics in the vicinity of these black holes are the Newtonian masses of the black holes even in the MOG theory. Consequently, shadow sizes increase as a function of the key dimensionless MOG parameter alpha that characterizes the variable gravitational coupling coefficient G, and may offer an observational means to distinguish the MOG theory from standard general relativity.