Dynamic population of locally admissible extremal critical branches

Determine whether a locally admissible extremal critical-particle branch in Kerr–Bertotti–Robinson spacetime can be populated dynamically through near-critical trajectories and physically realizable production mechanisms.

Background

The paper establishes that an exactly critical particle can support a locally admissible near-horizon branch around certain extremal Kerr–Bertotti–Robinson black holes, and that collisions with a usual ingoing particle on such a branch can produce divergent local effective center-of-mass energy. However, for the nonzero-field examples considered, the exactly critical particle cannot reach the extremal horizon by direct infall from infinity because finite-radius potential barriers obstruct the trajectory.

Consequently, the existence of a locally admissible branch does not show that the branch can actually be realized by particles supplied from an outer region. The unresolved issue is whether near-critical trajectories, together with a viable mechanism for producing them, can dynamically populate the branch and thereby make the local divergence physically attainable.