Effect of a weak electromagnetic field on particle acceleration by a rotating black hole

We study high energy charged particle collisions near the horizon in an electromagnetic field around a rotating black hole and reveal the condition of the fine-tuning to obtain arbitrarily large center-of-mass (CM) energy. We demonstrate that the CM energy can be arbitrarily large as the uniformly magnetized rotating black hole arbitrarily approaches maximal rotation under the situation that a charged particle plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. Recently, Frolov [Phys. Rev. D 85, 024020 (2012)] proposed that the CM energy can be arbitrarily high if the magnetic field is arbitrarily strong, when a particle collides with a charged particle orbiting the ISCO with finite energy near the horizon of a uniformly magnetized Schwarzschild black hole. We show that the charged particle orbiting the ISCO around a spinning black hole needs arbitrarily high energy in the strong field limit. This suggests that Frolov’s process is unstable against the black hole spin. Nevertheless, we see that magnetic fields may substantially promote the capability of rotating black holes as particle accelerators in astrophysical situations.

Figure 1

The dependence of the ISCO radius $r_{\mathrm{I}}$ on $b$ for some fixed value of $a_{*}$.

Figure 2

Panels (a), (b), and (c) show the energy of a charged particle as the function of the radius of a circular orbit for $b=0$, 1, and 10, respectively. The solid, dotted, dashed, thick, and dot-dashed curves in each panel denote the cases $a=0$, 0.25, 0.5, 0.99, and 1, respectively.