Acoustic black holes in curved spacetime and the emergence of analogue Minkowski spacetime

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.