κ-Poincaré dispersion relations and the black hole radiation

Following the methods developed by Corley and Jacobson, we consider qualitatively the issue of Hawking radiation in the case when the dispersion relation is dictated by quantum κ-Poincaré algebra. This relation corresponds to field equations that are non-local in time, and, depending on the sign of the parameter κ, to sub- or superluminal signal propagation. We also derive the conserved inner product, that can be used to count modes, and therefore to obtain the spectrum of black hole radiation in this case.