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The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Bañados-Silk-West (BSW) effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a highenergy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy-extraction efficiency is bounded by 2.19 approximately. On the other hand, if a very massive particle is produced as a result of the high-energy collision, which has negative energy and necessarily falls into the black hole, the upper limit of the energy-extraction efficiency is increased to (2 + √ 3) 2 ≃ 13.9. Thus, higher efficiency of the energy extraction, which is typically as large as 10, provides strong evidence for the production of a heavy particle.

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 consider a particle collision with a high center-of-mass energy near a Bañados-TeitelboimZanelli (BTZ) black hole. We obtain the center-of-mass energy of two general colliding geodesic particles in the BTZ black hole spacetime. We show that the center-of-mass energy of two ingoing particles can be arbitrarily large on an event horizon if either of the two particles has a critical angular momentum and the other has a non-critical angular momentum. We also show that the motion of a particle with a subcritical angular momentum is allowed near an extremal rotating BTZ black hole and that a center-of-mass energy for a tail-on collision at a point can be arbitrarily large in a critical angular momentum limit.

We consider the escape probability of a photon emitted from the innermost stable circular orbit (ISCO) around a rapidly rotating black hole. As an isotropically emitting light source on a circular orbit reduces its orbital radius, the escape probability of a photon emitted from it decreases monotonically. The escape probability evaluated at the ISCO decreases monotonically as the black hole spin increases. When the dimensionless Kerr parameter a is the Thorne limit a = 0.998, the escape probability at the ISCO is 58.8%.In the extremal case a = 1, even if the orbital radius of the light source is arbitrarily close to the ISCO radius, which coincides with the horizon radius, the escape probability remains at 54.6%. We also show that such photons that have escaped from the vicinity of the horizon reach infinity with sufficient energy because Doppler blueshift due to the proper motion of a source can overcome the gravitational redshift. Our findings indicate that if the M87 galactic center is a rapidly rotating black hole, signs of the near-horizon physics will be detectable on the edge of the black hole shadow. * Electronic address: igata@rikkyo.ac.jp † Electronic address: nakashi@rikkyo.ac.jp