Towards Thermodynamics of Universal Horizons in Einstein-æther Theory

Abstract

Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons," which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.

Non-relativistic holography from Hořava gravity

“…If these same arguments can be applied to black holes of Hořava gravity, the notion of holography naturally extends to a much larger class of theories, most notably those of an intrinsic non-relativistic nature [49,14,15,56,57,39]. Beyond this, such solutions are extremely important in holography: black holes geometries at a Hawking temperature T H are dual to thermal field theory states at the same temperature, as was know very early on in AdS/CFT [40,69,88].…”

“…The existence of causal horizons in Hořava gravity begs the question of whether they obey a thermodynamic description as do their counterparts in GR [19,14,15].…”

Asymptotically hyperbolic black holes in Horava gravity

“…If these same arguments can be applied to the universal horizons of Hořava gravity then the notion of holography naturally extends to a much larger class of theories, most notably those of an intrinsic non-relativistic nature [1,2,11,12,19,20].…”

“…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.…”

“…This gives a dispersion that is similar to the Schrödinger equation. Proceeding with the traditional methods of calculating ImS, one obtains the temperature of a static spherically symmetric black hole in Hořava gravity [12,25]: 26) where s M is the outward pointing space-like vector orthogonal to u M , a M ≡ u N ∇ N u M , and χ M = (1, 0, 0, 0) is the asymptotically time-like Killing vector. For the above analytic solution eq.…”