Lense-Thirring Effect as Viscous Vorticity and Gravitomagnetic Drag in the Dynamic Substrate Theory

Abstract The Lense-Thirring effect, or gravitational frame-dragging, represents one of the most subtle predictions of Einstein's General Relativity, classically attributed to off-diagonal components of the spacetime metric induced by mass-energy currents. Within standard geometric frameworks, interpreting this dragging mechanism inside an empty void presents conceptual challenges regarding the nature of inertia and momentum transfer. In this work, we address frame-dragging through the Dynamic Substrate Theory (DST), modeling the physical vacuum as a continuous, memory-endowed Maxwell-Oldroyd-B viscoelastic fluid. We demonstrate that the rotation of massive bodies does not twist an abstract geometric manifold; rather, it generates a physical field of viscous vorticity and shear-stress torques within the cosmic substrate. By solving the creeping flow momentum equations under Maxwell-Oldroyd-B rheology, we recover the exact classical gravitomagnetic precession frequencies for test gyroscopes without requiring geometric spacetime dragging. Keywords: Lense-Thirring Effect, Frame-Dragging, Viscoelastic Vacuum, Maxwell-Oldroyd-B Rheology, Gravitomagnetism, Substrate Fluid Dynamics.