Hořava gravity versus thermodynamics: The black hole case

Abstract

Under broad assumptions breaking of Lorentz invariance in gravitational theories leads to tension with unitarity because it allows for processes that apparently violate the second law of thermodynamics. The crucial ingredient of this argument is the existence of black hole solutions with the interior shielded from infinity by a causal horizon. We study how the paradox can be resolved in the healthy extension of Hořava gravity. To this aim we analyze classical solutions describing large black holes in this theory with the emphasis on their causal structure. The notion of causality is subtle in this theory due to the presence of instantaneous interactions. Despite this fact, we find that within exact spherical symmetry a black hole solution contains a space-time region causally disconnected from infinity by a surface of finite area -the 'universal horizon'.We then consider small perturbations of arbitrary angular dependence in the black hole background. We argue that aspherical perturbations destabilize the universal horizon and, at non-linear level, turn it into a finite-area singularity. The causal structure of the region outside the singularity is trivial. If the higher-derivative terms in the equations of motion smear the singularity while preserving the trivial causal structure of the solutions, the thermodynamics paradox would be obviated. As a byproduct of our analysis we prove that the black holes do not have any non-standard long-range hair. We also comment on the relation with Einstein-aether theory, where the solutions with universal horizon appear to be stable.

Asymptotically hyperbolic black holes in Horava gravity

“…The existence of causal horizons in Hořava gravity begs the question of whether they obey a thermodynamic description as do their counterparts in GR [10][11][12]. Motivation for such a description follows from arguments analogous to Bekenstein's original proposals [13]: a causal horizon must have intrinsic entropy if the second law is not to be violated when exterior entropy falls in.…”

“…Consistency with a first law then implies a temperature of the horizon. For Hořava gravity, additional motivation comes from its claim as a UV complete quantum theory of gravity [10]. From a microscopic description, the entropy of a macroscopic system is a measure of the number of fundamental degrees of freedom contained.…”

“…The convergence of its leaves is an invariant statement, and such a region is a causal boundary. Such a slice (that isn't asymptotic infinity) is called a "universal horizon" [6,9,10]: an event behind it cannot influence events outside as they are all at "earlier" times as measured by the preferred foliation. Solutions to Hořava gravity with universal horizons will be called black holes.…”

“…An interesting class of manifolds to examine with this technique are those which are black holes of GR [10]. These are defined by having event horizons: null causal boundaries of the asymptotic region.…”

Non-relativistic holography from Hořava gravity

“…The convergence of its leaves is an invariant statement, and such a region is a causal boundary. Such a slice (that isn't asymptotic infinity) is called a "universal horizon" [29,11,19]: an event behind it cannot influence events outside as they are all at "earlier" times as measured by the preferred foliation. Solutions to Hořava gravity with universal horizons will be called black holes, and explored in the next chapter.…”