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.

Figures (3)

• Figure 1: Plots of $g_{rr}^{-1}(r)$ (blue), $N^2 (r)$ (orange), $g_{\phi \phi}$ (green), and $g_{tt}$ (red) for the zero-mass $KAdS_4$ metric with the hyperbolic horizon topology (\ref{['KAdS4']}). Here, we plotted $\Lambda=-1, \theta=\pi/3$ with $a=1$ (left) and $a=0.1$ (right) for a comparison. The left panel shows the existence of an ergosphere (\ref{['ergo_KAdS']}) outside the event horizon $r_H=\sqrt{3/(-{\Lambda})}$. The right panel shows the shrunk ergosphere as the rotation parameter $a$ approaches to zero.
• Figure 2: Plots of $g_{rr}^{-1}(r)$ (blue), $N^2 (r)$ (orange), $g_{\phi \phi}$ (green), and $g_{tt}$ (red) for the zero-mass $KdS_4$ metric with the spherical horizon topology (\ref{['KdS4']}). Here, we plotted $\Lambda=1, \theta=\pi/3$ with $a=1$ (left) and $a=0.1$ (right). The left panel shows the existence of an ergosphere (\ref{['ergo_KdS']}) inside the cosmological horizon $r_C=\sqrt{3/{\Lambda}}$. The right panel shows the shrunk ergosphere as the rotation parameter $a$ approaches to zero.
• Figure 3: Plots of the ergospheres for zero-mass $KAdS_4$ metric (\ref{['KAdS4']}) with the hyperbolic horizon topology (blue region) and zero-mass $KdS_4$ metric (\ref{['KdS4']}) with the spherical horizon topology (orange region). Here, we plotted ${\Lambda}=\pm 1, a=1$ and the green line denotes the black hole horizon $r_H=\sqrt{3/(-{\Lambda})}$ or the cosmological horizon $r_C=\sqrt{3/{\Lambda}}$, and the blue and orange lines denote the corresponding ergosurfaces $r_{\rm erg (H)}$ and $r_{\rm erg (C)}$.