Ultra-high energy particle collisions in a regular spacetime without blackholes or naked singularities

TL;DR

This paper demonstrates that ultra-high energy particle collisions can occur in completely regular spacetimes without blackholes or naked singularities, expanding the understanding of particle acceleration in general relativity.

Contribution

It introduces conditions under which high-energy collisions happen in regular spacetimes, independent of blackholes or naked singularities, and provides a concrete example with Bardeen spacetime.

Findings

High-energy collisions require a maximum in the norm of the timelike Killing vector.

Such collisions can occur in spacetimes with a regular center and specific energy condition violations.

The Bardeen spacetime exemplifies the theoretical conditions for ultra-high energy particle acceleration.

Abstract

We investigate here the particle acceleration and collisions with extremely large center of mass energies in a perfectly regular spacetime containing neither singularity nor an event horizon. The ultra-high energy collisions of particles near the event horizon of extremal Kerr blackhole, and also in many other examples of extremal blackholes have been investigated and reported recently. We studied an analogous particle acceleration process in the Kerr and Reissner-Nordstrom spacetimes without horizon, containing naked singularities. Further to this, we show here that the particle acceleration and collision process is in fact independent of blackholes and naked singularities, and can happen in a fully regular spacetime containing neither of these. We derive the conditions on the general static spherically symmetric metric for such a phenomena to happen. We show that in order to have ultra-high energy collisions it is necessary for the norm of the timelike Killing vector to admit a maximum with a vanishingly small but a negative value. This is also a condition implying the presence of a surface with extremely large but nevertheless finite value of the redshift or blueshift. Conditions to have ultrahigh energy collisions and regular center imply the violation of strong energy condition near the center while the weak energy condition is respected in the region around the center. Thus the central region is surrounded by a dark energy fluid. Both the energy conditions are respected at the location where the high energy collisions take place. As a concrete example we then investigate the acceleration process in the spacetime geometry derived by Bardeen which is sourced by a non-liner self-gravitating magnetic monopole.