New Spinor Fields on Lorentzian 7-Manifolds

TL;DR

This paper classifies and constructs new classes of spinor fields on 7-dimensional Lorentzian manifolds, overcoming previous obstructions and linking these fields to geometric and physical properties like Killing vectors.

Contribution

It introduces conditions on spinor fields in Lorentzian 7-manifolds that enable the existence of new classes of spinors, expanding the classification beyond previous Riemannian results.

Findings

New spinor classes are explicitly constructed.

These spinors can define generalized current densities.

They can generate time Killing vectors at infinity.

Abstract

This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. The previously investigated Riemannian case is characterized by either one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general complex case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, these spinors can define a generalized current density which further defines a time Killing vector at the spatial infinity.