Slowly Rotating Black Hole Solutions to Ho\v{r}ava-Lifshitz Gravity

Abstract

We present a new stationary solution to the field equations of Ho\v{r}ava-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 L\"{u}, 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.