General limitations on trajectories suitable for super-Penrose process

Collisions of particles near a rotating black hole can lead to unbound energies $E_{c.m.}$ in their centre of mass frame. There are indications that the Killing energy of debris at infinity can also be unbound for some scenarios of collisions near the extremal black hole horizon (so-called super-Penrose process). They include participation of a particle that (i) has generic (not fine-tuned) parameters and (ii) moves away from a black hole before collision. We show that for any finite particle's mass, such a particle cannot be obtained as a result of the preceding collision. However, this can be done if one of initial infalling particles has the mass of the order $N^{-2}$ that generalizes previous observations made in literature for radial infall in the Kerr background.

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