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We show that Lorentzian manifolds whose isometry group is of dimension at least ½ n ( n −1)+1 admit different vector fields resulting in expanding, steady and shrinking Ricci solitons. Moreover, it is proved that those Ricci solitons are gradient (only) in the steady case. This provides examples of complete locally conformally flat and symmetric Lorentzian gradient Ricci solitons that are not rigid.

Ricci solitons on Lorentzian manifolds with large isometry groups