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

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In this paper, we study static vacuum solutions of quantum gravity at a fixed Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in closed forms in the infrared limit.

• The exact solutions represent spacetimes with very rich structures: they can represent generalized BTZ black holes, Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of any kind of space-time singularities, depending on the choices of the free parameters of the solutions.
• We also find several classes of exact static non-diagonal solutions, which represent similar space-time structures as those given in the diagonal case.
• The relevance of these solutions to the non-relativistic Lifshitz-type gauge/gravity duality is discussed.