Newtonian analogue of corresponding spacetime dynamics of rotating black holes: Implication on black hole accretion

TL;DR

This paper introduces a Newtonian potential that mimics key relativistic features of Kerr spacetime, including frame dragging, enabling simplified analysis of black hole accretion with reasonable accuracy.

Contribution

A novel velocity-dependent Newtonian potential for Kerr spacetime that accurately reproduces relativistic effects like frame dragging and orbital frequencies, especially for low to moderate spins.

Findings

Reproduces GR energy deviations within ~10% for circular orbits near rapidly spinning black holes.

Accurately models GR epicyclic frequencies with some deviations.

Replicates GR effects like perihelion precession and light bending reasonably well.

Abstract

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.