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In this paper, we study static vacuum solutions of quantum gravity at a fixedLifshitz point in (2+1) dimensions, and present all the diagonal solutions inclosed forms in the infrared limit. The exact solutions represent spacetimeswith very rich structures: they can represent generalized BTZ black holes,Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free ofany kind of space-time singularities, depending on the choices of the freeparameters of the solutions. We also find several classes of exact staticnon-diagonal solutions, which represent similar space-time structures as thosegiven in the diagonal case. The relevance of these solutions to thenon-relativistic Lifshitz-type gauge/gravity duality is discussed.

Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point