Universality of BSW mechanism for spinning particles

Ba\~nados $et\, al.$ (BSW) found that Kerr black holes can act as particle accelerators with collisions at arbitrarily high center-of-mass energies. Recently, collisions of particles with spin around some rotating black holes have been discussed. In this paper, we study the BSW mechanism for spinning particles by using a metric ansatz which describes a general rotating black hole. We notice that there are two inequivalent definitions of center-of-mass (CM) energy for spinning particles. We mainly discuss the CM energy defined in terms of the worldline of the particle. We show that there exists an energy-angular momentum relation $e = \Omega_h j$ that causes collisions with arbitrarily high energy near-extremal black holes. We also provide a simple but rigorous proof that the BSW mechanism breaks down for nonextremal black holes. For the alternative definition of the CM energy, some authors find a new critical spin relation that also causes the divergence of the CM mass. However, by checking the timelike constraint, we show that particles with this critical spin cannot reach the horizon of the black hole. Further numerical calculation suggests that such particles cannot exist anywhere outside the horizon. Our results are universal, independent of the underlying theories of gravity.Comment: 8 pages, 1 figure

Holographic complexity of the electromagnetic black hole

In this paper, we use the "complexity equals action" (CA) conjecture to evaluate the holographic complexity in some multiple-horzion black holes for F(Riemann) gravity coupled to a first-order source-free electrodynamics. Motivated by the vanishing result of the purely magnetic black hole founded by Goto $et.\, al$, we investigate the complexity in a static charged black hole with source-free electrodynamics and find that this vanishing feature of the late-time rate is universal for a purely static magnetic black hole. However, this result shows some unexpected features of the late-time growth rate. We show how the inclusion of a boundary term for the first-order electromagnetic field to the total action can make the holographic complexity be well-defined and obtain a general expression of the late-time complexity growth rate with these boundary terms. We apply our late-time result to some explicit cases and show how to choose the proportional constant of these additional boundary terms to make the complexity be well-defined in the zero-charge limit. For the static magnetic black hole in Einstein gravity coupled to a first-order electrodynamics, we find that there is a general relationship between the proper proportional constant and the Lagrangian function h(\math{F}) of the electromagnetic field: if h(\math{F}) is a convergent function, the choice of the proportional constant is independent on explicit expressions of h(\math{F}) and it should be chosen as $4/3$; if h(\math{F}) is a divergent function, the proportional constant is dependent on the asymptotic index of the Lagrangian function.Comment: 27 pages, 1 figure, some examples and references adde