Killing spinors as a characterisation of rotating black hole spacetimes

TL;DR

This paper demonstrates that the presence of Killing spinors in vacuum or electrovacuum spacetimes uniquely characterizes Kerr and Kerr-Newman black hole solutions, providing an alternative to curvature-based characterizations.

Contribution

It establishes that Killing spinors, combined with certain asymptotic conditions, can uniquely identify Kerr and Kerr-Newman spacetimes, offering a new characterization method.

Findings

Killing spinors imply the spacetime is locally Kerr or Kerr-Newman.

The characterization aligns with previous curvature-based results.

The approach applies to vacuum and electrovacuum solutions.

Abstract

We investigate the implications of the existence of Killing spinors in a spacetime. In particular, we show that in vacuum and electrovacuum a Killing spinor, along with some assumptions on the associated Killing vector in an asymptotic region, guarantees that the spacetime is locally isometric to the Kerr or Kerr-Newman solutions. We show that the characterisation of these spacetimes in terms of Killing spinors is an alternative expression of characterisation results of Mars (Kerr) and Wong (Kerr-Newman) involving restrictions on the Weyl curvature and matter content.