Slowly rotating black hole solutions to Hořava-Lifshitz gravity

We present a new stationary solution to the field equations of Hořava-Lifshitz gravity with the detailed balance condition and for any value of the coupling constant $\lambda >1/3$. This is the generalization of the corresponding spherically symmetric solution earlier found by Lü, Mei, and Pope to include a small amount of angular momentum. For the relativistic value $\lambda =1$, the solution describes slowly rotating AdS type black holes. With a soft violation of the detailed balance condition and for $\lambda =1$, 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.