Wormhole solutions to Hořava gravity

We present wormhole solutions to Hořava nonrelativistic gravity theory in vacuum. We show that, if the parameter $\lambda$ is set to one, traversable wormholes connecting two asymptotically de Sitter or anti-de Sitter regions exist. In the case of arbitrary $\lambda$, the asymptotic regions have a more complicated metric with constant curvature. We also show that, when the detailed balance condition is violated softly, traversable and asymptotically Minkowski, de Sitter or anti-de Sitter wormholes exist.

Figure 1

In this plot the relation between the horizons and the reflection point is shown, for the case $\lambda =1$, ${ϵ}_1={ϵ}_2=0$. As can be seen in the plot, the radius of the outer horizon, when it is present, is always larger than that of the reflection point, implying that a traversable wormhole must be constructed from a solution with a naked singularity.