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

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.