Black hole accretion in scalar-tensor-vector gravity

We examine the accretion of matter onto a black hole in scalar--tensor--vector gravity (STVG) also known as modified gravity (MOG). The gravitational constant is \(G=G_{N} (1 + \alpha)\) where \(\alpha\) is a parameter taken to be constant for static black holes in the theory. The MOG black hole is spherically symmetric and characterised by two event horizons. The matter falling into the black hole obeys the polytrope equation of state and passes through two critical points before entering the outer horizon. We obtain analytical expressions for the mass accretion rate as well as for the outer critical point, critical velocity and critical sound speed. Our results complement existing strong field tests like lensing and orbital motion and could be used in conjunction to determine observational constraints on MOG.