  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 non-relativistic counterpart. Relativistic condensates exhibit two
(rather than one) quasi-particle 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.
