Magnetic Penrose process in the magnetized Kerr spacetime

It is well established that the magnetic Penrose process (MPP) could be highly efficient (efficiency can even exceed 100%) for extracting the energy from a Kerr black hole, if it is immersed in a mG order magnetic field. Considering the exact solution of the magnetized Kerr spacetime, here we derive the exact expression of efficiency (ηMPP) for MPP, which is valid for both the Kerr black hole (BH) as well as Kerr superspinar (SS), and also from the weak magnetic field to an ultrastrong magnetic field (B) which can even distort the original Kerr geometry. We show that although the value of ηMPP increases up to a certain value of ultrastrong magnetic field (Bp), it decreases to zero for B>Bp, in case of the Kerr BHs. On the other hand, ηMPP shows the opposite behavior in case of the Kerr SSs. One intriguing feature that emerges is, ηMPP acquires the maximum value for the Kerr parameter a∗≈0.786 (unlike a∗=1 for the ordinary Penrose process), decreases for the range 0.786<a∗≤1, and reaches to 20.7% for a∗=1 with a few limitations. This indicates that the BH starts to expel the effect of magnetic field for a∗>0.786, and is fully expelled from the extremal Kerr BH due to the gravitational Meissner effect. As a special case of MPP, we also study the ordinary Penrose process (PP) for the magnetized Kerr spacetime. We show that the efficiency of PP decreases with increasing the magnetic field for the Kerr BH. In case of the Kerr SS, the efficiency of PP decreases from 103% to 0 for increasing the value of magnetic field from 0 to a specific value of ultrastrong magnetic field. Thus, the MPP for Kerr BHs, Kerr SSs and the ordinary PP for Kerr SSs can be superefficient for the astrophysical applications to powering engines in the high-energy sources like active galactic nuclei and quasars, in the weak magnetic fields. Our strong magnetic field result of MPP could be important to the primordial BHs in the early Universe immersed in the primordial magnetic fields, and to the transmuted BHs which are formed by collapsing and/or by merging of the magnetized progenitors. It is almost impossible to extract the energy from a BH (SS) through MPP (PP) in the ultrastrong magnetic fields.