Collisions of massive and massless particles around rotating black holes: general analysis

TL;DR

This paper analyzes particle collisions near rotating black holes, revealing conditions under which infinite energy in the center of mass frame occurs, based on kinematic effects involving gravitational blue shift and Doppler shift.

Contribution

It provides a general analysis of collisions between massive and massless particles near rotating black holes, identifying conditions for infinite energy outcomes and offering a kinematic explanation.

Findings

Infinite energy in the center of mass frame occurs under specific critical conditions.

The effect depends on the interplay of gravitational blue shift and Doppler effects.

Different particle pair combinations are systematically analyzed.

Abstract

We consider collisions between massive (electrons) and massless (photons) particles near the horizon of a rotating black hole. Similarly to collisions between massive particles, the infinite energy in the centre of mass frame occurs in some situations. Namely, for one particle the relationship between the energy and angular momentum should have a special form ("critical" particle) whereas for the second one it should not hold ("usual" particle). All combinations of possible pairs of critical and usual particles are analyzed. 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. Thus, a pure kinematic explanation is suggested for the effect of infinitely growing energies in the centre of mass frame.