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.
Highlights
JHEP04(2021)255 with the desire to preserve background independence, led to the development of extensions of General Relativity which include, in vacuum, the dynamics of an “aether” field and not just of the metric
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 have shown in two alternative ways that the Hawking radiation characterizing a black hole endowed with a universal horizon is set by the effective surface gravity characterizing the peeling of physical null rays in its proximity eq (6.7)
Summary
16πG d4x |g| R+c1∇μUν ∇μU ν +c2(∇μU μ)2 +c3∇μU ν ∇ν U μ +c4aμaμ +λ(UμU μ −1) , (2.1). Later we will discuss the implications of retaining the full dispersion relation (2.13) Another important point on understanding the motion of observers in this space-time is the construction of physical free-falling trajectories, i.e the rays of massless fields coupled to the metric, and to the aether and endowed with a modified dispersion relation. The pair (u, v) defines the causal cone of an observer communicating with signals that travel at speed c(r) At this point, it is worth noting that the rays satisfy the modified dispersion relation (2.13) locally at every space-time point, none of the components of kμ are constant along the trajectories. It is worth to point that the mode itself is of order Λ, the solution is still under perturbative control, since it is given as an analytic expansion on Λ−1 with finite and non-vanishing radius of convergence
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