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 R3⋊R and E(1,1)⋊R. We show that some of these Ricci solitons are conformally Einstein and they may be expanding, steady or shrinkingOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureS