Analog gravity models describe linear fluctuations of fluids as a massless scalar field propagating on stationary acoustic spacetimes constructed from the background flow. In this paper, we establish that this paradigm generalizes to arbitrary order nonlinear perturbations propagating on dynamical analog spacetimes. Our results hold for all inviscid, spherically symmetric and barotropic nonrelativistic flows in the presence of an external conservative force. We demonstrate that such fluids always admit a dynamical description governed by a coupled pair of wave and continuity equations. We provide an iterative approach to solve these equations about any known stationary solution to all orders in perturbation. In the process, we show that there exists a dynamical acoustic spacetime on which nonlinear fluctuations of the mass accretion rate propagate. The dynamical acoustic spacetime has a well-defined causal structure and curvature, and we find a classical fluctuation relation for the horizon. We find that the spacetime can have acoustic horizons that grow as well as recede under perturbations, with the latter having no known black hole analog. As an example, we numerically investigate the Bondi flow solution subject to exponentially damped time dependent perturbations. We find that second and higher order classical perturbations possess an acoustic horizon that oscillates to a new size at late times. In particular, the case of a receding acoustic horizon is realized through “low frequency” perturbations. We discuss our results in the context of more general analog models and its potential implications on astrophysical accretion flows.

• Received 14 February 2022
• Accepted 6 May 2022

DOI:https://doi.org/10.1103/PhysRevD.106.025020