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Different classes of exact solutions for the BHT massive gravity theory areconstructed and analyzed. We focus in the special case of the purely quadraticLagrangian, whose field equations are irreducibly of fourth order and are knownto admit asymptotically locally flat black holes endowed with gravitationalhair. The first class corresponds to a Kerr-Schild deformation of Minkowskispacetime along a covariantly constant null vector. As in the case of GeneralRelativity, the field equations linearize so that the solution can be easilyshown to be described by four arbitrary functions of a single null coordinate.These solutions can be regarded as a new sort of pp-waves. The second class isobtained from a deformation of the static asymptotically locally flat blackhole, that goes along the spacelike (angular) Killing vector. Remarkably,although the deformation is not of Kerr-Schild type, the field equations alsolinearize, and hence the generic solution can be readily integrated. It isneither static nor spherically symmetric, being described by two integrationconstants and two arbitrary functions of the angular coordinate. In the staticcase it describes "black flowers" whose event horizons break the sphericalsymmetry. The generic time-dependent solution appears to describe a gravitonthat moves away from a black flower. Despite the asymptotic behaviour of thesesolutions at null infinity is relaxed with respect to the one for GeneralRelativity, the asymptotic symmetries coincide. However, the algebra of theconserved charges corresponds to BMS$_{3}$, but devoid of central extensions.The "dynamical black flowers" are shown to possess a finite energy. The surfaceintegrals that define the global charges also turn out to be useful in thedescription of the thermodynamics of solutions with event horizons.

Asymptotically flat black holes and gravitational waves in three-dimensional massive gravity