Acoustic Horizons and Superfluid Bose-Einstein Condensate (BEC) Analogues for Substrate Dynamics in the Dynamic Substrate Theory

Abstract A core challenge in formulating alternative frameworks to General Relativity is the experimental verification of high-energy phenomena, such as singularity resolution and vacuum non-linearities. Analogue gravity bridges this gap by utilizing condensed matter systems—specifically Bose-Einstein Condensates (BECs)—where acoustic perturbations experience an effective spacetime metric. This paper formulates the exact mapping between the Dynamic Substrate Theory (DST) viscoelastic vacuum and low-temperature superfluid acoustic analogues, demonstrating how laboratory BEC setups can simulate acoustic horizons, non-linear core saturation, and analogue Hawking radiation. Keywords: Analogue Gravity, Bose-Einstein Condensates, Acoustic Horizons, Maxwell-Oldroyd-B Vacuum, Dynamic Substrate Theory.