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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 λ> 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 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.