Acceleration of particles near the inner black hole horizon

TL;DR

This paper investigates the potential for particles to achieve unbounded collision energy near the inner horizon of black holes, analyzing different particle motion scenarios and the feasibility of infinite energy release.

Contribution

It demonstrates that infinite energy collisions are impossible, but arbitrarily large energies can be achieved under specific initial conditions, clarifying the limitations of the BSW effect near inner horizons.

Findings

Strong energy divergence is impossible due to horizon crossing constraints.

Large but finite collision energies are achievable with specific initial particle trajectories.

Particles starting inside the horizon can lead to unbounded collision energies.

Abstract

We study the possibility of obtaining unbound energy E_{c.m.} in the centre of mass frame when two particles collide near the inner black hole horizon. We consider two different cases - when both particles move (i) in the same direction or (ii) in the opposite ones. We also discuss two different versions of the effect - whether an infinite energy can be released in the collision (strong version) or the energy E_{c.m.} is finite but can be made as large as one likes (weak version). We demonstrate that the strong version of the effect is impossible in both cases (i) and (ii). In case (i) this is due to the fact that in the situation when E_{c.m.} formally diverges on the horizon, one of particles passes through the bifurcation point where two horizons meet while the second particle does not, so collision does not occur. In case (ii), both particles hit different branches of the horizon. The weak version is possible in both cases, provided at least one of particles starts its motion inside the horizon along the direction of spatial symmetry from infinity.