Four-dimensional Lorentzian plane symmetric static Ricci solitons

Abstract

Our focus is to investigate the Ricci solitons of the plane symmetric and static four-dimensional Lorentzian metrics. It is found that these metrics admit shrinking and concircular potential Ricci soliton vector fields with either 6- or 10-dimensional Lie algebra. Further, it is observed that the 4-dimensional Lorentzian static Ricci soliton manifolds are Einsteinian and hence the Ricci solitons are the trivial Ricci solitons.