Ricci solitons on four-dimensional Lorentzian Lie groups

We determine all non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups whose soliton vector field is left-invariant. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian metrics on semi-direct extensions R-3 (sic) R and E(1, 1) (sic) R. We show that some of these Ricci solitons are conformally Einstein and they may be expanding, steady or shrinking.

Automated summary

This article investigates non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups with left-invariant soliton vector fields. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian metrics on semi-direct extensions R-3 (sic) R and E(1, 1) (sic) R. It is shown that some of these Ricci solitons are conformally Einstein and can be expanding, steady, or shrinking.