Spinor-helicity and the algebraic classification of higher-dimensional spacetimes

TL;DR

This paper develops a spinor-based classification scheme for higher-dimensional spacetimes, specifically five-dimensional ones, unifying and clarifying previous classification methods used in general relativity.

Contribution

It introduces a novel spinor-helicity approach to classify higher-dimensional spacetimes, connecting and resolving issues between existing classification schemes.

Findings

Reproduces the structure of CMPP and de Smet classifications

Unifies different classification schemes for 5D spacetimes

Resolves longstanding questions about classification relationships

Abstract

The spinor-helicity formalism is an essential technique of the amplitudes community. We draw on this method to construct a scheme for classifying higher-dimensional spacetimes in the style of the four-dimensional Petrov classification and the Newman-Penrose formalism. We focus on the five-dimensional case for concreteness. Our spinorial scheme naturally reproduces the full structure previously seen in both the CMPP and de Smet classifications, and resolves longstanding questions concerning the relationship between the two classifications.