High-dimensional Lifshitz-type spacetimes, universal horizons, and black holes in Hořava-Lifshitz gravity

Abstract

In this paper, we present all [(d + 1) + 1]-dimensional static diagonal vacuum solutions of the non-projectable Hořava-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 ≤ z < 2 for d ≥ 3 and 1 ≤ z < ∞ for d = 2, due to the stability and ghost-free conditions of the theory.

Hořava gravity at a Lifshitz point: A progress report

“…Since they were first discovered in [202,215], universal horizons have been studied intensively, and already attracted lots of attention. These include universal horizons in static spacetimes [123,[218][219][220][221][222][223][224][225][226][227][228][229][230][231][232][233][234], and the ones with rotation [217,235,236] 25 . In particular, it was showed that universal horizons exist in the 24 To avoid theČerenkov effects, in the khronometric theory, or more general, in the Einstein-aether theory, c φ is required to be no less than the speed of light c φ ≥ c [203].…”

Horava-Lifshitz black hole hydrodynamics

“…For additional studies of these solutions, see [24][25][26][27]. In this case one adds a negative cosmological constant Λ to the action above…”

Thermal geometry from CFT at finite temperature

“…Actually, it was found that HL gravity is a minimal holographic dual for the field with Lifshitz scaling [25]. Our recent works [26,27] found that various Lifshitz spacetimes are possible even without matter fields. Therefore, in principle, extension of the cMERA to modified gravity is possible.…”