The Vortex Framework: Emergent Gravity and Strong-Field Dynamics Part III: Acoustic Metric, Phase-Rigidity Pressure, and Evacuated Core

Part III of the Vortex Framework trilogy extends the emergent particle and gauge theories of Parts I 1 and II 2 into the domain of gravitation. Using a superfluid substrate as a unifying medium, we derive an acoustic metric that mimics general relativistic behavior, including frame-dragging, and link the macroscopic phenomenon of gravity to the displacement of vortex networks. We introduce the concept of phaserigidity pressure as the ultimate resistance against gravitational collapse, leading to an evacuated-core model for spinning compact objects that naturally avoids singularities. Implications for black hole phenomenology, Hawking radiation, and experimental tests in analogue systems are discussed. Throughout, gravity is treated as an emergent, analogue phenomenon arising within an effective field theory regime; no claim is made that the present construction replaces or derives full general relativity at the microscopic level.