Acceleration of particles by black holes: kinematic explanation

TL;DR

This paper presents a kinematic explanation for how particles can achieve infinite energy in collisions near black hole horizons, emphasizing the roles of particle velocity and frame transformations.

Contribution

It introduces a simple, general kinematic framework explaining particle acceleration near black holes, applicable to both rotating and charged black holes, based on particle velocities and frame effects.

Findings

Infinite energy in particle collisions near horizons explained kinematically

Critical particles have finite frequency near the horizon, unlike usual particles

Classification of collision types based on particle criticality and mass

Abstract

A new simple and general explanation of the effect of acceleration of particles by black holes to infinite energies in the centre of mass frame is suggested. It is based on kinematics of particles moving near the horizon. This effect arises when particles of two kinds collide near the horizon. For massive particles, the first kind represents a particle with the generic energy and angular momentum (I call them "usual"). Near the horizon, such a particle has a velocity almost equal to that of light in the frame that corotates with a black hole (the frame is static if a black hole is static). The second kind (called "critical") consists of particles with the velocity v<c near the horizon due to special relationship between the energy and angular momentum (or charge). As a result, the relative velocity approaches the speed of light c, the Lorentz factor grows unbound. This explanation applies both to generic rotating black holes and charged ones (even for radial motion of particles). If one of colliding particles is massless (photon), the critical particle is distinguished by the fact that its frequency is finite near the horizon. The existence (or absence) of the effect is determined depending on competition of two factors - gravitational blue shift for a photon propagating towards a black hole and the Doppler effect due to transformation from the locally nonrotating frame to a comoving one. Classification of all possible types of collisions is suggested depending on whether massive or massless particle is critical or usual.