  We theoretically investigate the excitation dynamics in a photon-fluid with
both local and nonlocal interactions. We show that the interplay between
locality and an infinite-range nonlocality gives rise to a gapped Bogoliubov
spectrum of elementary excitations which, at lower momenta, correspond to
massive particles (phonons) with a relativistic energy-momentum relation. In
this regime and in the presence of an inhomogeneous flow the density
fluctuations are governed by the massive Klein-Gordon equation on the acoustic
metric and thus propagate as massive scalar fields on a curved spacetime. We
finally demonstrate that in the non-relativistic limit the phonon modes behave
as self-gravitating quantum particles with an effective Schr\"{o}dinger-Newton
dynamics, although with a finite-range gravitational interaction and a non-zero
cosmological constant. Our photon-fluid represents a viable alternative to BEC
models for "emergent-gravity" scenarios and offers a promising setting for
analogue simulations of quantum gravity phenomenology and semiclassical
gravity.
