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

TL;DR

This work extends the Bañados-Silk-West (BSW) analysis of high-energy particle collisions to nonequatorial trajectories near generic stationary axially symmetric black holes with a finite force. By performing near-horizon expansions of the metric functions and particle variables, and by analyzing acceleration in a comoving frame (CO) against OZAMO frames, the authors derive robust regularity conditions for usual, subcritical, critical, and ultracritical particles. A key result is that the polar velocity component $u^{\theta}$ stays finite, ensuring that nonequatorial motion does not qualitatively alter the BSW scenarios and allowing a unified description across different horizon types. The findings yield general, physically interpretable constraints (encoded in integers $p,q,k,l$ and exponents in expansions) and reveal belt-like regions in parameter space where certain collisions can occur, with results applicable to a wide range of astrophysical contexts beyond equatorial motion. Overall, the paper provides a comprehensive, frame-aware treatment of near-horizon particle dynamics under finite forces and establishes the persistence of high-energy collision mechanisms in broader settings."

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.