Circular orbits and acceleration of particles by near-extremal dirty rotating black holes: general approach

TL;DR

This paper investigates ultra-high energy particle collisions near near-extremal rotating black holes, revealing universal scaling laws for collision energy depending on surface gravity and orbit type, applicable to generic 'dirty' black holes.

Contribution

It generalizes the BSW effect analysis to generic dirty rotating black holes, establishing universal energy scaling laws and extending previous Kerr-specific results.

Findings

Collision energy scales as $rac{1}{rac{1}{3}}$ or $rac{1}{rac{1}{2}}$ depending on orbit type.

Near-horizon collision energy decreases as the collision point approaches the horizon.

Universal energy scaling laws apply to generic dirty rotating black holes, not just Kerr black holes.

Abstract

We study the effect of ultra-high energy particles collisions near the black hole horizon (BSW effect) for two scenarios: when one of particle either (i) moves on a circular orbit or (ii) plunges from it towards the horizon. It is shown that such circular near-horizon orbits can exist for near-extremal black holes only. This includes the innermost stable orbit (ISCO), marginally bound orbit (MBO) and photon one (PhO). We consider generic "dirty" rotating black holes not specifying the metric and show that the energy in the centre of mass frame has the universal scaling dependence on the surface gravity $\kappa $. Namely, $E_{c.m.}\sim \kappa ^{-n}$ where for the ISCO $n=1/3$ in case (i) or $n=1/2$ in case (ii). For the MBO and PhCO $n=1/2$ in both scenarios that agrees with recent calculations of Harada and Kimura for the Kerr metric. We also generalize the Grib and Pavlov's observations made for the Kerr metric. The magnitude of the BSW effect on the location of collision has a somewhat paradoxical character: it is decreasing when approaching the horizon.