Collisional super-Penrose process and Wald inequalities

TL;DR

This paper investigates high-energy particle collisions near naked singularities or potential barriers in axially symmetric spacetimes, analyzing energy relations, escape conditions, and implications for observable phenomena, extending previous Kerr metric results.

Contribution

It develops a general framework for analyzing particle collisions in various spacetimes, relating center-of-mass and Killing energies, and describes escape conditions and observable effects.

Findings

Unbounded energy at infinity is possible near horizon thresholds.

Different spacetime types exhibit distinct energy relations.

Results align with previous Kerr metric studies.

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).