  Based on the conserved Hamiltonian for a test particle, we have formulated a
Newtonian analogue of Kerr spacetime in the `low energy limit of the test
particle motion' that, in principle, can be comprehensively used to describe
general relativistic (GR) features of Kerr spacetime, however, with less
accuracy for high spin. The derived potential, which has an explicit velocity
dependence, contains the entire relativistic features of corresponding
spacetime including the frame dragging effect, unlike other prevailing
pseudo-Newtonian potentials (PNPs) 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 ~ 10 %
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, though with a relatively higher percentage of
deviation. For counterrotating cases, the obtained potential replicate 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 like perihelion advancement and bending of
light with reasonable accuracy. The formulated Kerr-Newtonian potential thus
can be useful to study complex accreting plasma dynamics and its implications
around rotating BHs in the Newtonian framework, avoiding GR gas dynamical
equations.
