Near-horizon behavior of nonequatorial accelerated particle motion and high energy particle collisions

TL;DR

This paper analyzes particle motion near black hole horizons, showing that high-energy collisions are qualitatively similar for equatorial and nonequatorial trajectories, with results applicable to various astrophysical scenarios.

Contribution

It extends the understanding of the BSW effect to nonequatorial particle motion, demonstrating the finiteness of the polar velocity component under general conditions.

Findings

Polar velocity remains finite near the horizon.

High-energy collision scenarios are similar for equatorial and nonequatorial motion.

Results are applicable to diverse astrophysical contexts.

Abstract

We consider motion of a particle in the background of a stationary axially symmetric generic black hole. A particle experiences the action of a force of unspecified nature. We require the force to remain finite in a comoving frame. The result is expressed in terms of several integers characterizing the Taylor expansion of the metric coefficients near the horizon. We show that the polar component of the four-velocity remains finite. As a result, the scenarios of high-energy particle collisions, found previously in the context of the BSW effect for equatorial motion, do not change qualitatively in the nonequatorial case. The fact that the polar component is finite, also enables us to fill some gaps in the description of the BSW effect in previous works. Our results have a quite general character and can be used not only in description of high energy particle collisions but also in diverse astrophysical problems for which motion is not constrained by the equatorial plane.