Work in particle physics and general relativity (GR) has established that deep connections exist between acoustics and GR. Most remarkable is the fact that acoustic wave propagation in fluids is governed by an effective Lorentzian spacetime geometry: Acoustic waves follow the geodesics of a (curved) acoustic metric. This provides an entirely new way of looking at acoustic propagation, and in principle provides valuable theoretical tools since much of the machinery developed by the GR community over the past several decades can be directly applied to acoustic systems expressed in this framework. Notably, supersonic liquid flows are predicted to have completely analogous properties to spacetime regions near (gravitational) black holes. We present the status of a developing research program at NRL, designed to begin exploring these connections via laboratory experiments, numerical simulations, and theoretical development. [Work supported by the Office of Naval Research.]