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

TL;DR

This paper introduces slowly rotating black hole solutions in Hořava-Lifshitz gravity, extending previous spherically symmetric solutions to include angular momentum, and calculates their mass and angular momentum.

Contribution

It generalizes known static solutions to include slow rotation and explores solutions under different conditions in Hořava-Lifshitz gravity.

Findings

Found slowly rotating AdS black hole solutions for λ=1.

Extended solutions to include small angular momentum.

Calculated mass and angular momentum of the solutions.

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.