High energy particle collisions near black holes

Abstract

Abstract. If two geodesic particles collide near a rotating black hole, their energy in the centre of mass frame E c.m. can become unbound under certain conditions (the so-called BSW effect). The special role is played here by so-called critical geodesics when one of particles has fine-tuned energy and angular momentum. The nature of geodesics reveals itself also in fate of the debris after collisions. One of particles moving to a remote observer is necessarily near-critical. We discuss, when such a collision can give rise not only unboud E c.m. but also unbound Killing energy E (so-called super-Penrose process).Investigation of high energy collisions of particles near black holes comes back to works [1] - [3]. In recent years, an interest to this issue revived after the observation made by Bañados, Silk and West (the BSW effect, after the names of its authors) that particle collision near the Kerr black hole can lead, under certain additional conditions, to the unbounded growth of the energy in their centre of mass E c.m. [4]. Later on, in a large series of works, this observation was generalized and extended to other objects and scenarios. The energy that appears in the BSW effect is relevant for an observer who is present just near the point of collision in the vicinity of the black hole horizon. Meanwhile, what is especially physically important is the Killing energy E of debris after such a collision measured by an observer at infinity. Strong redshift "eats" significant part of E c.m. , so it was not quite clear in advance, to what extent the energy E may be high. If E exceeds the initial energy of particles, we are faced with the energy extraction from a black hole. This is a so-called collisional Penrose process (the Penrose process that occurs due to particle collisions). Thus there are two related but different issues: (i) investigation of the effect of unbounded E c.m. , (ii) study of properties of E and the question about the maximum possible efficiency of the collisional Penrose process.Consider the generic axially symmetric metric. It can be written asHere, the metric coefficients do not depend on t and φ. On the horizon N = 0. Alternatively, one can use coordinates θ and r, similar to Boyer-Lindquist ones for the Kerr metric, instead of l and z. In (1) we assume that the metric coefficients are even functions of z, so the equatorial plane θ = π 2 (z = 0) is a symmetry one.In the space-time under discussion there are two conserved quantities u 0 ≡ −E and u φ ≡ L where u μ = dx μ dτ is the four-velocity of a test particle, τ is the proper time and x μ = (t, φ, l, z) are coordinates..The aforementioned conserved quantities have the physical meaning of the energy per unit mass (or frequency for a lightlike particle) and azimuthal component of the angular momentum,