Zero-Mass Rotating Spacetimes in Four-Dimensional Horava Gravity

Abstract

We study a particular exact solution for rotating spacetimes in four-dimensional Horava gravity, which has been proposed as a renormalizable gravity model without the ghost problem. We show that the zero-mass Kerr spacetime or the zero-mass Kerr-(A)dS spacetime in Einstein gravity is an exact solution in four-dimensional Horava for an arbitrary IR Lorentz-violation parameter lambda, but with an appropriate cosmological constant. In particular, for the zero-mass topological Kerr-AdS black hole solution with the hyperbolic horizon topology or the zero-mass Kerr-dS cosmological solution with the spherical horizon topology, there exist the ergosphere and the non-vanishing (positive) Hawking temperature, which imply the existence of negative mass black holes as well as positive mass spacetimes, by losing its mass from the zero-mass ones via the Hawking radiation or Penrose process in the ergosphere.