Hydrodynamic accretion on to a rapidly rotating Kerr black hole

Bondi-type hydrodynamic accretion of the surrounding matter on to a Kerr black hole with an arbitrary rotational parameter is considered. The effects of viscosity, thermal conductivity and interaction with radiation field are neglected. The black hole is supposed to be at rest with respect to matter at infinity. The flow is adiabatic and has no angular momentum. The fact that usually in astrophysics a substance far from the black hole has a non-relativistic temperature introduces a small parameter to the problem, and allows us to search for the solution as a perturbation of the accretion of cold (dust-like) matter. However, far from the black hole, on a scale of the order of the radius of the sonic surface, the expansion must be performed with respect to the Bondi spherically symmetrical solution for accretion on a Newtonian gravitating centre. The equations thus obtained are solved analytically. The conditions of the regularity of the solution at the sonic surface and at infinity allow us to specify a unique solution, to find the shape of the sonic surface and to determine the corrections to the Bondi accretion rate.