  Horava gravity is a proposal for completing general relativity in the
ultraviolet by interactions that violate Lorentz invariance at very high
energies. We focus on (2+1)-dimensional projectable Horava gravity, a theory
which is renormalizable and perturbatively ultraviolet-complete, enjoying an
asymptotically free ultraviolet fixed point. Adding a small cosmological
constant to regulate the long distance behavior of the metric, we search for
all circularly symmetric stationary vacuum solutions with vanishing angular
momentum and approaching the de Sitter metric with a possible angle deficit at
infinity. We find a two-parameter family of such geometries. Apart from the
cosmological de Sitter horizon, these solutions generally contain another
Killing horizon and should therefore be interpreted as black holes from the
viewpoint of the low-energy theory. Contrary to naive expectations, their
central singularity is not resolved by the higher derivative terms present in
the action. It is unknown at present if these solutions form as a result of
gravitational collapse. The only solution regular everywhere is just the de
Sitter metric devoid of any black hole horizon.
