Algebraic classification of five-dimensional spacetimes using scalar invariants

TL;DR

This paper applies algebraic classification methods based on scalar invariants and discriminants to five-dimensional spacetimes, demonstrating their effectiveness on complex metrics like black rings and solitons.

Contribution

It extends the discriminant approach for algebraic classification to more complex five-dimensional spacetimes, showing practical computation of discriminants.

Findings

Discriminant techniques can classify complex higher-dimensional spacetimes.

Useful algebraic information can be extracted from complicated metrics.

The approach is applicable to various five-dimensional solutions.

Abstract

There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alignment theory, bivectors and discriminants. Previous work gave a set of necessary conditions in terms of discriminants for a spacetime to be of a particular algebraic type. We demonstrate the discriminant approach by applying the techniques to the Sorkin-Gross-Perry soliton, the supersymmetric and doubly-spinning black rings and some other higher dimensional spacetimes. We show that even in the case of some very complicated metrics it is possible to compute the relevant discriminants and extract useful information from them.