Slowly rotating black hole solutions to Horava-Lifshitz gravity

We present a new stationary solution to the field equations of Horava-Lifshitz gravity with the detailed balance condition and for any value of the coupling constant λ>1/3. This is the generalization of the corresponding spherically symmetric solution earlier found by Lue, Mei, and Pope to include a small amount of angular momentum. For the relativistic value λ=1, the solution describes slowly rotating AdS type black holes. With a soft violation of the detailed balance condition and for λ=1, we also find such a generalization for the Schwarzschild type black hole solution of the theory. Finally, using the canonical Hamiltonian approach, we calculate the mass and the angular momentum of these solutions.