Causal character of imaginary Killing spinors and spinorial slicings

TL;DR

This paper characterizes spin initial data saturating the BPS bound in asymptotically AdS spaces, introducing criteria for imaginary Killing spinors and constructing spinorial slicings, with implications for black holes and gravitational waves.

Contribution

It provides a new criterion for replacing imaginary Killing spinors with strictly timelike or null ones and demonstrates spinors' use in constructing codimension-2 slicings.

Findings

Characterization of BPS-saturating spin initial data in AdS

A theorem for replacing mixed causal type spinors

Construction of codimension-2 spinorial slicings

Abstract

We characterize spin initial data sets that saturate the BPS bound in the asymptotically AdS setting. This includes both gravitational waves and rotating black holes in higher dimensions, and we establish a sharp dimension threshold in each case. A key ingredient in our argument is a theorem providing a general criterion for when an imaginary Killing spinor of mixed causal type can be replaced by one that is strictly timelike or null. Moreover, in analogy with the minimal surface method, we demonstrate that spinors can be used to construct a codimension-$2$ slicing.