High-dimensional Lifshitz-type spacetimes, universal horizons and black holes in Ho\v{r}ava-Lifshitz gravity

In this paper, we present all $[(d+1)+1]$-dimensional static diagonal vacuum solutions of the non-projectable Ho\v{r}ava-Lifshitz gravity in the IR limit, and show that they give rise to very rich Lifshitz-type structures, depending on the choice of the free parameters of the solutions. These include the Lifshitz spacetimes with or without hyperscaling violation, Lifshitz solitons, and black holes. Remarkably, even the theory breaks explicitly the Lorentz symmetry and allows generically instantaneous propagations, universal horizons still exist, which serve as one-way membranes for signals with any large velocities. In particular, particles even with infinitely large velocities would just move around on these boundaries and cannot escape to infinity. Another remarkable feature appearing in the Lifshitz-type spacetimes is that the dynamical exponent $z$ can take its values only in the ranges $1\le z<2$ for $d\ge 3$ and $1\le z<\mathrm{\infty }$ for $d=2$, due to the stability and ghost-free conditions of the theory.