On type II(D) Einstein spacetimes in six dimensions

TL;DR

This paper reviews recent advances in classifying six-dimensional Einstein spacetimes of type II, revealing that the most general solutions are Kerr-Schild type D metrics characterized by specific parameters.

Contribution

It extends the classification of Einstein spacetimes to six dimensions, identifying the most general solutions under certain conditions as Kerr-Schild type D metrics.

Findings

Most general six-dimensional type D Einstein metric is Kerr-Schild.

Characterization involves one discrete and three continuous parameters.

Connections to known Kerr-(A)dS and Kerr-NUT-(A)dS metrics are clarified.

Abstract

After a concise overview of Einstein spacetimes of type II (or more special) in four and five dimensions, we summarize recent results in the six-dimensional case. We assume the optical matrix to be non-degenerate and ``generic'', and the Weyl tensor to fall off sufficiently rapidly at infinity. As it turns out, the most general metric is characterized by one discrete (normalized) and three continuous parameters, is of type D and belongs to the Kerr-Schild class. Its relation to the previously known Kerr-(A)dS and Kerr-NUT-(A)dS metrics is clarified.