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.
We examine bound orbits of particles around singly rotating black rings. We show that there exist stable bound orbits in toroidal spiral shape near the 'axis' of the ring, and also exist stable circular orbits on the 'axis' as special cases. The stable bound orbits can have arbitrary large size if the thickness of the ring is less than a critical value.
We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches 5/12 and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching 2GM/c 2 , where M is the mass of the black hole. When two particles collide and produce two particles in the ergoregion of a rotating black hole, one of the produced particles can escape to infinity with energy larger than the total energy of the particles before the collision, which is called the collisional Penrose process [1,2]. In 2009, Bañados, Silk, and West showed that the centerof-mass energy of two colliding particles can be arbitrarily large if they collide near the event horizon of an extremal Kerr black hole and one of the colliding particles has the critical value of the angular momentum [3]. This is called the Bañados-Silk-West effect. In recent years, this type of particle collision and the maximum of the energy-extraction efficiency have been investigated [4][5][6][7][8][9]. If one of the colliding particles has the critical angular momentum and both of the colliding particles come from infinity, the energy-extraction efficiency can reach ≃ 14 [6], which is exactly given by (2+ √ 3) 2 [7-9]. Berti, Brito, and Cardoso showed that the efficiency of the collisional Penrose process becomes arbitrarily large, if two subcritical particles collide head on near the horizon [10]. This is called the super-Penrose process. In this case, a radially outward particle must be created near the horizon by some preceding process. For example, particle emission and radiation from a collapsing star and an accretion disk as well as multiple scattering of infalling particles 1 can generate radially outward particles in the ergoregion.The existence of near-extremal Kerr black holes is suggested by x-ray observations [11]. Therefore, the study of the super-Penrose process is important not only as one of the basic properties of an extremal Kerr black hole but also from a point of view of observational astrophysics.In this paper, we present an analytic formulation to investigate the energy-extraction efficiency and the escape * Email: k.ogasawara@rikkyo.ac.jp † Email: harada@rikkyo.ac.jp ‡ Email: umpei@akita-pu.ac.jp § Email: igata@rikkyo.ac.jp 1 Leiderschneider and Piran discuss that considering multiple collision of particles from infinity, the net energy extraction efficiency is 14 at most [E. Leiderschneider and T. Piran, 2015].probability o...
We study bound orbits of a free particle around a singly rotating black ring. We find there exists chaotic motion of a particle which is gravitationally bound to the black ring by using the Poincaré map.PACS numbers: 04.50.Gh I. INTRODUCTIONChaos is one of the characteristic behavior of non-linear dynamical systems. In the context of general relativity, there are two main issues concerning chaos. One is chaotic oscillations which generally occur in the early stage of the universe near the initial singularity [1,2]. The other is chaotic motion of particles around black holes. There appears chaotic behavior of charged particles around a magnetized black hole[3], particles around a gravitationally perturbed black hole[4], a spinning particle around a black hole in vacuum [5], and particles around multi-black holes [6].Recently, general relativity in higher dimensions gathers much attention in relation to modern unified theories of interactions. Properties of the gravitational field depend on the spacetime dimensions critically. As for the cosmological models, the chaotic oscillations of the early universe disappear in higher dimensions [7]. As for the black holes, in five dimensions, exact solutions of a black ring with the horizon topology of S 2 × S 1 are discovered by Emparan and Reall[8] in addition to rotating black holes with the spherical horizon topology obtained by Myers and Perry [9].The geodesic motion of a test particle is one of the most important probes for spacetime geometry because it reveals the geometrical difference of the black ring and the black hole. It is known that Myers-Perry black holes in any dimensions allow separation of variables in the Hamilton- * Electronic address: igata@sci.osaka-cu.ac.jp
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