In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose-Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their nonrelativistic counterpart. Relativistic condensates exhibit two (rather than one) quasiparticle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show that the metric associated with the massless mode is a generalization of the usual acoustic geometry allowing also for non-conformally flat spatial sections. This is relevant, as it implies that these systems can allow the simulation of a wider variety of geometries. Finally, while in non-RBECs the transition is from Lorentzian to Galilean relativity, these systems represent an emergent gravity toy model where Lorentz symmetry is present (albeit with different limit speeds) at both low and high energies. Hence they could be used as a test field for better understanding the phenomenological implications of such a milder form of Lorentz violation at intermediate energies.

Local and non-local properties of Hawking radiation in the presence of short distance dispersion are computed using connection formulae. The robustness of the spectrum and that of the two-point function are explained by showing that the leading deviations from the relativistic expressions decrease with the inverse of the spatial extension of the near horizon region. This region corresponds to a portion of de Sitter space with a preferred frame. We show that the phases of the Bogoliubov coefficients are relevant for the two-point function in black and white holes, and also for the black hole laser effect. We also present an unexpected relation between the spectra obtained with sub and with superluminal dispersion and we apply our formalism to massive fields. Our predictions are validated by numerical analysis.