Ray tracing Einstein-Æther black holes: Universal versus Killing horizons

Abstract

Violating Lorentz-invariance, and so implicitly permitting some form of superluminal communication, necessarily alters the notion of a black hole. Nevertheless, in both Einstein-AEther gravity, and Hořava-Lifshitz gravity, there is still a causally disconnected region in black-hole solutions; now being bounded by a "Universal horizon", which traps excitations of arbitrarily high velocities. To better understand the nature of these black holes, and their Universal horizons, we study ray trajectories in these spacetimes. We find evidence that Hawking radiation is associated with the Universal horizon, while the "lingering" of ray trajectories near the Killing horizon hints at reprocessing there. In doing this we solve an apparent discrepancy between the surface gravity of the Universal horizon and the associated temperature derived by tunneling method. These results advance the understanding of these exotic horizons, and provide hints for a full understanding of black-hole thermodynamics in Lorentz-violating theories.

Dispersion relation and surface gravity of universal horizons

“…In this paper, we reconsider ray tracing [29] in Einstein-aether black hole spacetime, and find that, instead of the results of Cropp et al, the surface gravity of the universal horizon is indeed dependent on the power z, hence for the associated Hawking temperature. These findings may be important for the full understanding Lorentz-violating theories.…”

“…Another different viewpoint is in [27], in which the late time radiation was computed. Cropp et al [29] studied ray tracing, found the evidence of Hawking radiation at universal horizon and ray lingering near Killing horizon and, gave the covariant definition of surface gravity of universal horizon. However, it is incorrect that the surface gravity they obtained is independent of the specific dispersion relations, see Appendix for more details.…”

Non-relativistic holography from Hořava gravity

“…The temperature derived via the tunneling method for z φ = 2 has recently been reproduced in [24] by arguments concerning ray tracing near the universal horizon and their relation to the surface gravity. It is claimed this calculation is universal regardless of the exact dispersion, but that would contradict the tunneling method in the z φ → ∞ limit.…”

“…23) 24) are obtained, where it is understood that this is a matching of the asymptotic r → 0 fields. The vanishing of the O(c 2 ) term of the dtdx i piece yields the restriction …”

Asymptotically hyperbolic black holes in Horava gravity

“…The temperature derived via the tunneling method for z φ = 2 has recently been reproduced in [30] by arguments concerning ray tracing near the universal horizon and their relation to the surface gravity. It is claimed this calculation is universal regardless of the exact dispersion, but that would contradict the tunneling method in the z φ → ∞ limit.…”