Doubly Torqued Vectors and a classification of Doubly Twisted and Kundt spacetimes

TL;DR

This paper introduces doubly torqued vectors to classify and characterize various spacetime types, including doubly twisted, warped, and Kundt spacetimes, highlighting their properties and symmetries.

Contribution

It provides a novel framework using doubly torqued vectors for classifying and understanding spacetime geometries and their symmetries.

Findings

Doubly torqued vectors characterize doubly twisted and Kundt spacetimes.

Timelike vectors relate to doubly twisted and warped spacetimes.

Null vectors relate to Kundt and PP wave spacetimes.

Abstract

The simple structure of doubly torqued vectors allows for a natural characterization of doubly twisted down to warped spacetimes, as well as Kundt spacetimes down to PP waves. For the first ones the vectors are timelike, for the others they are null. We also discuss some properties, and their connection to hypersurface orthogonal conformal Killing vectors, and null Killing vectors.