Carrollian Motion in Magnetized Black Hole Horizons

TL;DR

This paper explores how massless particles with anyonic spin can move within black hole horizons due to magnetic fields, revealing a novel spin-Hall effect influenced by Carroll symmetries and magnetic monopoles.

Contribution

It demonstrates a corrected magnetic field invariant under Carroll diffeomorphisms and extends the spin-Hall effect analysis to weakly charged rotating black holes in magnetic fields.

Findings

Magnetic field is not Carroll invariant in previous models.

A Carroll-invariant magnetic field configuration is identified.

Spin-Hall effect occurs even without black hole rotation.

Abstract

We revisit the motion of massless particles with anyonic spin in the horizon of Kerr--Newman geometry. As recently shown, such particles can move within the horizon of the black hole due to the coupling of charges associated with a 2-parametric central extension of the 2-dimensional Carroll group to the magnetic field generated by the black hole -- the so called "anyonic spin-Hall effect". We show that the previously computed magnetic field is not invariant under Carroll diffeomorphisms and find another result which respects these symmetries of the horizon. We also consider a more astrophysically relevant case of a (weakly charged) rotating back hole placed in a uniform magnetic field, which could, for instance, be induced by the surrounding plasma. We show that a qualitatively similar magnetic field assisted anyonic spin-Hall effect takes place, even in the absence of black hole rotation. The theoretical possibility of a motion induced by a magnetic monopole is also studied.