High energy collision of two particles in wormhole spacetimes

Abstract

We study the collision of two particles in the Teo wormhole spacetime, in which the wormhole is stationary and axisymmetric. We show that a non-rotating Teo wormhole cannot be a particle accelerator, while a rotating Teo wormhole can be used to accelerate particles and create high energy collisions because of the deep effective potential of the colliding particles. The process is different from that in the vicinity of a near-extremal black hole, since here there is no event horizon. This is the first example of particle collision with high center-of-mass energy in a spacetime with no event horizon, no naked singularity, and not being extremal in a clear sense. The process can unlikely have direct implications for astrophysical observations, but it is interesting as a tool to investigate wormhole instabilities.

Collisional super-Penrose process and Wald inequalities

“…(17), (18) for the metric below). Astrophysical significance of this situation is still unclear, but it can happen, in particular, for wormholes [26]- [29]. In this limit both for massless (4) and massive (13) fragments we find that the maximum energy at infinity is given by the same formulae (5) and (14), so that…”

“…Using the expressions for sin θ L , cos θ L , sin θ , cos θ from (52,53,59,60), the definitions of E, P, P r , P φ , M from Eqs. (24)(25)(26)(27)(28)(29)(30)(31)(32), and some more algebra, we can obtain θ E ≡ θ L + θ :…”

“…It is clear from Eqs. (26), (30) and (32) that for the same energies and angular momenta of the colliding particles, the energy in the center of mass frame is greater when they are traveling in the opposite directions in the radial coordinate. Indeed, when Z 1 Z 2 < 0, the absolute values of Z 0 and P are less than when Z 1 Z 2 > 0, while X 0 and E stay the same, which leads to greater M in (32).…”

Super-Penrose process and rotating wormholes

“…First of all, this includes wormholes. For the first time, high energy collisions in wormhole space-times were considered in [6] where it was shown for a particular model (the Teo wormhole [7]) that unbounded E c.m. is possible.…”

“…To achieve our goal, it is necessary that particle 3 escape to infinity without reflection from the potential barrier back to the vicinity of the throat, so that the expression inside the radical in (6) should be positive everywhere. Then, the condition under discussion reads Z 2 > 0, where Z is given by (6). To simplify formulas, let us assume that m 3 = 0 or negligible.…”