Near-horizon circular orbits and extremal limit for dirty rotating black holes

TL;DR

This paper investigates the properties of near-horizon circular orbits around generic rotating black holes with matter, highlighting differences between extremal and near-extremal cases and their implications for high-energy collisions.

Contribution

It extends previous Kerr black hole results to generic dirty rotating black holes, analyzing orbit behavior near extremality and their relation to high-energy collision phenomena.

Findings

Near-horizon orbits can approach the horizon arbitrarily closely in near-extremal black holes.

On-horizon circular orbits are impossible for massive particles in extremal black holes.

Properties of orbits relate to the Ba ext~nados-Silk-West effect and kinematic censorship.

Abstract

We consider generic rotating axially symmetric "dirty" (surrounded by matter) black holes. Near-horizon circular equatorial orbits are examined in two different cases of near-extremal (small surface gravity $\kappa $) and exactly extremal black holes. This has a number of qualitative distinctions. In the first case, it is shown that such orbits can lie as close to the horizon as one wishes on suitably chosen slices of space-time when $\kappa \rightarrow 0$. This generalizes observation of T.\ Jacobson Class. Quantum Grav. 28 187001 (2011) made for the Kerr metric. If a black hole is extremal ($\kappa =0$), circular on-horizon orbits are impossible for massive particles but, in general, are possible in its vicinity. The corresponding black hole parameters determine also the rate with which a fine-tuned particle on the noncircular near-horizon orbit asymptotically approaches the horizon. Properties of orbits under discussion are also related to the Ba% \~nados-Silk-West effect of high energy collisions near black holes. Impossibility of the on-horizon orbits in question is manifestation of kinematic censorship that forbids infinite energies in collisions.