A Slowly Rotating Black Hole in Horava-Lifshitz Gravity and a 3+1 Dimensional Topological Black Hole: Motion of Particles and BSW Mechanism

TL;DR

This paper investigates particle motion and the BSW mechanism near slowly rotating and topological Lifshitz black holes in Horava-Lifshitz gravity, finding that the BSW effect does not occur due to finite collision energies.

Contribution

It provides a detailed analysis of geodesics and particle collisions in these specific black hole spacetimes, highlighting the absence of the BSW effect.

Findings

Effective potential analysis of particle orbits

Finite center-of-mass energy at the horizon

BSW mechanism not observed in these black holes

Abstract

The motion of a neutral particle in the vicinity of a slowly rotating black hole in the Horava-Lifshitz theory of gravity and 3+1 dimensional topological Lifshitz black hole is investigated. Geodesics for radial motion of the particles are also plotted. Some different cases of the orbital motion of the particle are discussed where maximum and minimum values of the effective potential are calculated. Further the Ba\~{n}ados, Silk and West (BSW) mechanism is studied for these black holes. It is shown that the centre-of-mass energy (CME) of two colliding uncharged particles at the horizon of these black holes remains finite. Thus the BSW effect cannot be seen in these cases.