Analog gravity describes fluctuations of hydrodynamic systems in terms of a massless scalar field propagating on curved spacetimes. This analogy between hydrodynamic and gravitational systems remains largely unexplored for nonlinear dynamical effects. In this paper, we provide the first description of dynamical analog spacetimes up to arbitrary order nonlinear perturbations constructed about stationary solutions. We find a high frequency response that exhibit known properties of perturbed black holes, as well as a low frequency regime for analog spacetimes with novel characteristics. Our framework more generally describes nonlinear perturbations of compressible hydrodynamic systems as analogs of nonlinear wave phenomena on black hole spacetimes.

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• Classical black holes
• Gravitation
• Interactions in fluids