We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.Comment: 8 pages, double-column; This version: references updated; added another example in section III. This version matches the published versio

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.

Abstract:We use the asymptotic data at conformal null-infinity I to formulate Weinberg's soft-photon theorem for Abelian gauge theories with massless charged particles. We show that the angle-dependent gauge transformations at I are not merely a gauge redundancy, instead they are genuine symmetries of the radiative phase space. In the presence of these symmetries, Poisson bracket between gauge potentials is not well-defined. This does not pose an obstacle for the quantization of the radiative phase space, which proceeds by treating the conjugate electric field as the fundamental variable. Denoting by G + and G − as the group of gauge transformations at I + and I − respectively, Strominger has shown that a certain diagonal subgroup G diag ⊂ G + × G − is the symmetry of the S-matrix and Weinberg's soft-photon theorem is the corresponding Ward identity. We give a systematic derivation of this result for Abelian gauge theories with massless charged particles. Our derivation is a slight generalization of the existing derivations since it is applicable even when the bulk spacetime is not exactly flat, but is only "almost" Minkowskian.