Escape probability of the super-Penrose process

Abstract: We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches $5/12$ and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching $2GM/c^2$, where $M$ is the mass of the black hole.