Slowly rotating black hole solutions to Hořava-Lifshitz gravity

We present a new stationary solution to the field equations of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity with the detailed balance condition and for any value of the coupling constant $\ensuremath{\lambda}>1/3$. This is the generalization of the corresponding spherically symmetric solution earlier found by L\"u, Mei, and Pope to include a small amount of angular momentum. For the relativistic value $\ensuremath{\lambda}=1$, the solution describes slowly rotating AdS type black holes. With a soft violation of the detailed balance condition and for $\ensuremath{\lambda}=1$, 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.

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