Maximal efficiency of the collisional Penrose process with spinning particles

We analyze the collisional Penrose process of spinning test particles in an extreme Kerr black hole. We consider that two particles plunge into the black hole from infinity and collide near the black hole. For the collision of two massive particles, if the spins of particles are ${s}_{1}\ensuremath{\approx}0.01379\text{ }\text{ }\ensuremath{\mu}M$ and ${s}_{2}\ensuremath{\approx}\ensuremath{-}0.2709\text{ }\text{ }\ensuremath{\mu}M$, we obtain the maximal efficiency is about ${\ensuremath{\eta}}_{\mathrm{max}}=(\text{extracted energy})/(\text{input energy})\ensuremath{\approx}15.01$, which is more than twice as large as the case of the collision of non-spinning particles (${\ensuremath{\eta}}_{\mathrm{max}}\ensuremath{\approx}6.32$). We also evaluate the collision of a massless particle without spin and a massive particle with spin (Compton scattering), in which we find the maximal efficiency is ${\ensuremath{\eta}}_{\mathrm{max}}\ensuremath{\approx}26.85$ when ${s}_{2}\ensuremath{\approx}\ensuremath{-}0.2709\text{ }\text{ }\ensuremath{\mu}M$, which should be compared with ${\ensuremath{\eta}}_{\mathrm{max}}\ensuremath{\approx}13.93$ for the nonspinning case.

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