Limitations on the Penrose process

It is well known that the Penrose process (PP) is a way for extracting energy from a black hole (BH). An analytical and partially numerical study of the PP is presented for a particular case: an incoming particle, at rest at infinity, decays into two photons inside the ergoregion of a Kerr BH, assuming that all particles follow equatorial orbits. It is shown that this process cannot exist if the angular momentum of the BH is lower than a critical value. Considering the features of the non equatorial Kerr geodesics, it is conjectured that even when the incoming particle is not at rest at infinity and the trajectories are not equatorial, the critical value still holds. This lower limit on the angular momentum implies that not all the rotational energy of the BH could be extracted with the Penrose processes that we have considered.