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 quantum vortices as 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 also be simulated and the derivations presented here have some deep connections with the holographic principle.