Effective potential approach to study hydrodynamics and particle dynamics in Kerr geometry

TL;DR

This paper derives an effective potential in Kerr geometry that accurately models relativistic features, enabling simplified analysis of particle and accretion disk dynamics around rotating black holes.

Contribution

The authors present an exact effective potential for Kerr spacetime that replicates relativistic effects and simplifies the study of particle motion and accretion disk precession.

Findings

Effective potential accurately mimics relativistic features across all spin parameters.

The potential captures key particle trajectory behaviors in Kerr spacetime.

Application to accretion disk studies demonstrates its practical utility.

Abstract

We derive the exact form of effective potential in Kerr geometry from the general relativistic radial momentum equation. The effective potential accurately mimics the general relativistic features, over the entire range of the spin parameter $-1<a<1$. We obtain the exact expression of the rate of dragging of inertial frames that can be used to study the relativistic precession of twisted accretion disks that are formed when the disk outskirts are tilted relative to the equatorial plane of the black hole. We then present an effective potential that provides a simplistic approach to study particle dynamics using physical concepts analogous to the Newtonian physics. We compare the equatorial as well as off-equatorial particle trajectories obtained using our potential with the general relativistic solutions. We find that our approach can capture the salient features of Kerr geometry and is applicable to studies of accretion processes around Kerr black holes.