Collisional super-Penrose process and Wald inequalities

Abstract

We consider collision of two massive particles in the equatorial plane of an axially symmetric stationary spacetime that produces two massless particles afterwards. It is implied that the horizon is absent but there is a naked singularity or another potential barrier that makes possible the head-on collision. The relationship between the energy in the center of mass frame E c.m. and the Killing energy E measured at infinity is analyzed. It follows immediately from the Wald inequalities that unbounded E is possible for unbounded E c.m. only. This can be realized if the spacetime is close to the threshold of the horizon formation. Different types of spacetimes (black holes, naked singularities, wormholes) correspond to different possible relations between E c.m. and E. We develop a general approach that enables us to describe the collision process in the frames of the stationary observer and ZAMO (zero angular momentum observer). The escape cone and escape fraction are derived. A simple explanation of the existence of the bright spot is given. For the particular case of the Kerr metric, our results agree with the previous ones found in M. Patil, T. Harada, K. Nakao, P.S. Joshi, and M. Kimura, Phys. Rev. D 93, 104015 (2016

Center of mass energy of colliding electrically neutral particles and super-Penrose process

“…For example, in the Kerr and Kerr-Newman background dω + dr < 0 for extremal black holes and slightly overspinning metrics -e.g., see Fig. 1 and discussion in [21] and Fig. 2 in [27].…”

“…It was observed in [20] for the overspinned Kerr metric that if m 0 is finite, no SPP occurs. This was generalized and explained in terms of the Wald identities [25] in [21]. In this sense, the absence of the SPP is clear in advance.…”

“…There are different objects and scenarios with these features. Particle 1 can bounce back from the potential barrier existing in the case of naked singularity and collide with an ingoing particle 2 [19], [20], [21]. Then, considering reflection from the potential barrier and making transformation between the original stationary frame, LNRF (locally nonrotating frame) and the CM one, we obtain for generic rotating axially symmetric over-spinned space-time that E 3 can be unbounded, so the SPP does occur -see Sec.…”

“…Then, considering reflection from the potential barrier and making transformation between the original stationary frame, LNRF (locally nonrotating frame) and the CM one, we obtain for generic rotating axially symmetric over-spinned space-time that E 3 can be unbounded, so the SPP does occur -see Sec. 3.5 of [21]. In another version, particles 1 and 2 can come from the opposite mouths of a wormhole [26], [22].…”

“…Now, we are in position to show that the dependence (31) itself leads to the SPP, independently of the details of the scenario. In doing so, our approach is simpler than in [21] since we are using one frame only.…”