The shocks during the accretion of an ultrarelativistic supersonic gas onto a rotating black hole

In this work, we track the evolution of an ultrarelativistic fluid onto a Kerr black hole, on the equatorial plane. In this treatment, we consider the limit where the rest mass density is neglected, that is, the approximation is valid in the regime where the internal energy dominates over the rest mass density. We particularly concentrate in the case of a gas with $\Gamma$ = 4/3, which corresponds to a radiation fluid. We show, as in several cases, that a shock cone appears when the asymptotic velocity of the fluid is larger than the asymptotic relativistic sound speed of the gas. On the other hand, in order to show the system approaches to steady state, we calculate the accreted total energy rate on a spherical surface. Finally, we also show the gas distribution and various of its properties.