New fermions in the bulk

TL;DR

This paper classifies spinor fields in 5-dimensional Lorentzian manifolds, discovering new classes with potential applications in bulk fermions and brane-world models, and constructs a Killing vector field related to these spinors on Kerr black hole horizons.

Contribution

It generalizes the 4D Lounesto classification to 5D, introduces new spinor classes, and links them to black hole horizons and bulk fermion localization.

Findings

New classes of 5D spinor fields identified.

Quaternionic bilinear covariants used to derive spin density.

Constructed Killing vector field connects black hole horizon to infinity.

Abstract

Spinor fields on 5-dimensional Lorentzian manifolds are classified, according to the geometric Fierz identities that involve their bilinear covariants. Based upon this classification that generalises the celebrated 4-dimensional Lounesto classification of spinor fields, new non-trivial classes of 5-dimensional spinor fields are, hence, found, with important potential applications regarding bulk fermions and their subsequent localisation on brane-worlds. In addition, quaternionic bilinear covariants are used to derive the quaternionic spin density, through the truncated exterior bundle. In order to accomplish a realisation of these new spinors, a Killing vector field is constructed on the horizon of 5-dimensional Kerr black holes. This Killing vector field is shown to reach the time-like Killing vector field at the spatial infinity, through a current 1-form density, constructed with the derived new spinor fields. The current density is, moreover, expressed as the f\"unfbein components, assuming a condensed form.