The structure of the Ricci tensor on locally homogeneous Lorentzian   gradient Ricci solitons
  We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show the soliton is rigid in dimensions three and four. In the steady case, we give a complete classification in dimension three. 
M. Brozos-V\'azquez, E. Garc\'ia-R\'io, P. Gilkey, and S.   Gavino-Fern\'andez
math.DG