Particle acceleration by Majumdar–Papapetrou di-hole

Abstract

We explore the multi-black hole spacetimes from the perspective of the ultra-high energy particle collisions. Such a discussion is limited to the spacetimes containing a single black hole so far. We deal with the Majumdar-Papapetrou solution representing a system consisting of two identical black holes in the equilibrium. In order to identify the conditions suitable for the process of high energy collisions, we consider particles confined to move on the equatorial plane towards the axis of symmetry with the zero angular momentum. We consider collision between the particles moving in opposite directions at the location midway between the black holes on the axis. We show that the center of mass energy of collision between the particles increases with the decrease in the separation between the black holes and shows divergence in the limit where the separation goes to zero. We estimate the size of the region close to the central point on the equatorial plane where it would be possible to have high energy collisions and show that this region has a reasonably large spatial extent. We further explore the process of high energy collisions with the general geodesics with arbitrary angular momentum on the equatorial plane away from the central point. Although in this paper we deal with the Majumdar-Papapetrou spacetime which serves as a toy example representing multiple black holes, we speculate on the possibility that the ultra-high energy collisions would also occur in the more general setting like colliding black holes, when distance between the black holes is extremely small, which can in principle be verified in the numerical relativity simulations. M. Patil (B)

Ultra-high energy collisions in static space-times: single versus multi-black hole cases

“…This is just the example discussed in [5]. We compare the approach of [5] with ours and reveal that, actually, there are two different kinds of limits that lead to high energy collisions.…”

“…Two kinds of limiting transitions in revealed in Sec. VI, brief comparison with previous results on this subject [5] is made. In Sec.…”

“…Quite recently, new set-up was suggested in [5]. In that paper, collisions in the multiblack hole metric were studied.…”

“…was obtained for extremely small space separation between black holes. In doing so, different cases were compared in [5] to the BSW effect near a single black hole depending on the sign of radial velocities (whether particles move in the same direction or in the opposite one).…”

“…can be achieved near multi-black holes for collision of any two particles moving in the vicinity of multi-black hole metric (starting from the two black hole configuration). The angle ψ between their velocity can be arbitrary, in the case ψ = 0 or ψ = π we return to the situation considered in [5].…”