Hawking radiation from universal horizons

Abstract

The persistence of a suitable notion of black hole thermodynamics in Lorentz breaking theories of gravity is not only a non-trivial consistency test for such theories, it is also an interesting investigation per se, as it might help us identifying the crucial features at the root of these surprising laws governing such purely gravitational objects. In past investigations, controversial findings were presented in this sense. With the aim of settling this issue, we present here two complementary derivations of Hawking radiation in geometries endowed with universal horizons: a novel feature of back holes in Lorentz breaking theories of gravity which reproduces several properties normally characterizing Killing horizons. We find that both the derivations agree on the fact that the Hawking temperature associated to these geometries is set by the generalized universal horizon peeling surface gravity, as required for consistency with extant derivations of the first law of thermodynamics for these black holes. We shall also comment on the compatibility of our results with previous alternative derivations and on their significance for the survival of the generalized second law of black hole thermodynamics in Lorentz breaking theories of gravity.

Causality and Particle Production from Universal Horizons

“…A particular limit of (34) -where c 1 + c 4 = c 1 + c 3 = 0 -was explored in [14]. Comparing with them, we find perfect agreement for the same values of the couplings.…”

“…However, it is not clear if this naive approach is correct. Although there are works that point towards this direction [8][9][10][11][12][13][14], there are others that question this picture [15]. Among the positive results, the resulting Hawking temperature reads…”

“…If we demand U µ and all metric invariants to be of class C 2 , so that the action is welldefined, then the same must be demanded for N , owing to its scalar character. In this case, then (14) implies that N must change sign at the UH. This has an obvious consequence for a black hole -its interior and exterior are causally reversed.…”

“…where we have used N ∝ 1 + A(r uh ) 2 F (r uh ) = 0. In order to fix the value of v we follow [14]. Close to the UH the ray infinitely blue-shifts, its momentum becoming of order Λ [22].…”

Black hole surface gravity in doubly special relativity geometries

“…[24]). The UV completion of LIV theories could remedy at this problem by introducing further geometrical structure to the black holes (the so-called Universal Horizon [22]) which might fix a universal temperature and restore black hole thermodynamics [25].…”