Generalized pseudo-Newtonian potential for studying accretion disk dynamics in off-equatorial planes around rotating black holes: Description of a vector potential

We prescribe a pseudo-Newtonian vector potential for studying accretion disks around Kerr black holes. The potential is useful for studying the inner properties of a disk not confined to the equatorial plane where general relativistic effects are indispensable. Therefore, we incorporate the essential properties of the metric at the inner radii through the pseudo-Newtonian potential derived from the general Kerr spacetime. The potential, reproducing most of the salient features of general relativity, is valid for the entire regime of the Kerr parameter. It reproduces the last stable circular orbit exactly as that in the Kerr geometry. It also reproduces the last bound orbit and energy at the last stable circular orbit with a maximum error similar to 7% and similar to 15%, respectively, up to an orbital inclination 30 degrees.