  Different classes of exact solutions for the BHT massive gravity theory are
constructed and analyzed. We focus in the special case of the purely quadratic
Lagrangian, whose field equations are irreducibly of fourth order and are known
to admit asymptotically locally flat black holes endowed with gravitational
hair. The first class corresponds to a Kerr-Schild deformation of Minkowski
spacetime along a covariantly constant null vector. As in the case of General
Relativity, the field equations linearize so that the solution can be easily
shown 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 is
obtained from a deformation of the static asymptotically locally flat black
hole, that goes along the spacelike (angular) Killing vector. Remarkably,
although the deformation is not of Kerr-Schild type, the field equations also
linearize, and hence the generic solution can be readily integrated. It is
neither static nor spherically symmetric, being described by two integration
constants and two arbitrary functions of the angular coordinate. In the static
case it describes "black flowers" whose event horizons break the spherical
symmetry. The generic time-dependent solution appears to describe a graviton
that moves away from a black flower. Despite the asymptotic behaviour of these
solutions at null infinity is relaxed with respect to the one for General
Relativity, the asymptotic symmetries coincide. However, the algebra of the
conserved charges corresponds to BMS$_{3}$, but devoid of central extensions.
The "dynamical black flowers" are shown to possess a finite energy. The surface
integrals that define the global charges also turn out to be useful in the
description of the thermodynamics of solutions with event horizons.
