Studies of accretion flows around rotating black holes - I. Particle dynamics in a pseudo-Kerr potential

In this series of papers, we shall present a simplistic approach to the study of particle dynamics, fluid dynamics and numerical simulations of accretion flows and outflows around rotating black holes. We show that with a suitably modified effective potential of the central gravitating rotating object, one can carry out these studies very accurately. In this approach, one need not use the full general relativistic equations to obtain the salient features of the general relativistic flows provided the Kerr parameter remains within -1 <= a <= 0.8. We present the equatorial and the non-equatorial particle trajectories from our potential and compare salient properties in Kerr and in pseudo-Kerr geometries. Our potential naturally produces accurate results for motions around the Schwarzschild geometry when the black hole angular momentum is set to zero.