High energy collision of particles in the vicinity of extremal black holes in higher dimensions: Bañados-Silk-West process as linear instability of extremal black holes

Abstract

We study high energy particle collisions around higher dimensional black holes. It is shown that the center of mass energy can be arbitrarily large in the vicinity of the event horizon like the Bañados, Silk and West (BSW) process in four dimensions if the following two conditions are satisfied: (i) the horizon is extremal and (ii) the parameters of either of the two colliding particles are fine-tuned, which is called a critical particle condition. We also show that a test particle which satisfies the critical particle condition can reach the event horizon from a distant region for a simple case. Finally, we discuss the relation between the BSW process and the linear instability of test fields around extremal black holes, the latter of which has been recently found by Aretakis [25][26][27][28][29][30].

Particle collision with an arbitrarily high center-of-mass energy near a Bañados-Teitelboim-Zanelli black hole

“…The effect of a weak electromagnetic field on the BSW collision [7] and the BSW collision in the near-horizon geometry of the extremal Kerr black hole spacetime were discussed [8]. Two ingoing neutral particle collide with an arbitrarily large center-of-mass energy in a near horizon limit not only in the extremal Kerr black hole spacetime but also in the Kerr-Newmann spacetime [9], in the Kerr naked singularity spacetime [10] in the Kerr-de Sitter black hole spacetime [11], in higher dimensional black hole spacetimes [12,13], and in lower dimensional black hole spacetimes [14][15][16][17].…”

Kinematics of two-particle scattering in black hole backgrounds

“…It is by now established that the effect of the unboundedness in the center-of-mass energy in certain kinematical domains are a universal property of classical particle kinematics in the background of asymptotically flat black holes [2], [16]. The issue of the divergence of the center of mass-energy is also extended to the collision of the two particles in the background of Sen black hole [17] and higher dimensional Kerr black hole geometry [18], [19].…”

High energy collision of two particles in wormhole spacetimes

“…The BSW effect has been also studied in a variety of near-extremal black hole spacetimes [14,20], including cases in higher dimensions [16,21], and some nearextremal non-black-hole spacetimes [22,23]. These recent studies have revealed that the BSW effect is a universal property in extremal and near-extremal spacetimes, while particle accelerations would also occur in non-near-extremal spacetimes if a gravitational potential is deep [6].…”

“…From the relativistic point of view, high energy collisions of particles on curved spacetimes are interesting because the phenomenon would have close relationships with other relativistic effects, such as the emission of gravitational waves [13], the self-gravity of colliding objects [14], and instabilities of the background spacetime [14][15][16]. In astrophysical situations, the true upper bound of the center-of-mass energy for a particle collision would be affected by these relativistic effects.…”

“…This implies that extremal black holes are unstable against the BSW process. Tsukamoto et al [16] showed that there are analogies between the instability of extremal horizons suggested by the BSW effect and the test-field instability of extremal horizons studied by Aretakis [24].…”