# Acoustic black holes in curved spacetime and emergence of analogue Minkowski metric

## TL;DR

This paper explores how analogue gravity models can be realized in curved spacetimes using relativistic field theories, revealing emergent acoustic metrics and connections to holography.

## Contribution

It demonstrates the emergence of acoustic metrics in curved spacetimes via relativistic theories and links flat Minkowski spacetime to Anti-de Sitter space through perturbations.

## Key findings

- Acoustic metrics can be derived from curved spacetime models.
- Minkowski spacetime can be simulated from Anti-de Sitter space.
- Quantum vortices' energy ratios evaluated during gravitational binding.

## Abstract

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.