Newtonian analogue of corresponding space-time dynamics of rotating black holes: implication for black hole accretion

Based on the conserved Hamiltonian for a test particle, we have formulated a Newtonian analogue of Kerr space-time in the 'low energy limit of the test particle motion'. In principle, this can be used comprehensively to describe general relativistic (GR) features of Kerr space-time, but with less accuracy for high spin. The derived potential, which has an explicit velocity dependence, contains the entire relativistic features of corresponding space-time, including the frame dragging effect, unlike other prevailing pseudo-Newtonian potentials for the Kerr metric where such an effect is either totally missing or introduced in a ad hoc manner. The particle dynamics with this potential precisely reproduce the GR results within a maximum similar to 10 per cent deviation in energy for a particle orbiting circularly in the vicinity of a rapidly corotating black hole. GR epicyclic frequencies are also well reproduced with the potential, although with a relatively higher percentage of deviation. For counter-rotating cases, the obtained potential replicates the GR results with precise accuracy. The Kerr-Newtonian potential also approximates the radius of marginally stable and marginally bound circular orbits with reasonable accuracy for a < 0.7. Importantly, the derived potential can imitate the experimentally tested GR effects, such as perihelion advancement and bending of light with reasonable accuracy. Thus, the formulated Kerr-Newtonian potential can be useful to study complex accreting plasma dynamics and its implications around rotating black holes in the Newtonian framework, avoiding GR gas dynamical equations.