  Gravity is not only able to be mimicked in flat spacetimes, but also in
curved spacetimes. We study analogue gravity models in curved spacetime by
considering the relativistic Gross-Pitaevskii theory and Yang-Mills theory in
the fixed background spacetime geometry. The results show that acoustic metrics
can be emergent from curved spacetimes yielding a Hadamard product of a real
metric-tensor and an analogue metric-tensor. Taking \emph{quantum vortices} as
\emph{test particles}, we evaluate their released energy ratio during the
"gravitational binding". The $2+1$-dimensional flat Minkowski metric is derived
from the $3+1$-dimensional Anti-de Sitter space by considering perturbations of
the Yang-Mills field, which implies that Minkowski spacetime can be also
simulated and the derivations presented here have some deep connections with
the holographic principle.
