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 superfluidsubstrate as a unifying medium, we derive an acoustic metric that mimics general relativistic behavior, including frame-dragging, and link the macroscopic phenomenonof gravity to the displacement of vortex networks. We introduce the concept of phaserigidity pressure as the ultimate resistance against gravitational collapse, leading to anevacuated-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.
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