Topological Conduits and Wormhole Stability via Viscoelastic Shear Resistance in the Maxwell-Oldroyd-B Vacuum

Abstract The geometric formulation of General Relativity models gravitation and space-time topology as the curvature of a pseudo-Riemannian manifold. While extraordinarily successful in macroscopic celestial mechanics, this approach encounters fundamental limitations at extreme scales, requiring ad-hoc constructs such as singularities and unphysical exotic matter to stabilize topological structures like wormholes (Einstein-Rosen bridges). The Dynamic Substrate Theory (DST) offers a paradigm shift by replacing the inert geometric void with a physical, compressible, and viscoelastic continuous medium. By modeling the vacuum through Maxwell-Oldroyd-B rheology, we introduce intrinsic material properties to space itself: memory, relaxation, and elastic shear resistance. In this work, we demonstrate that topological conduits are stabilized naturally by massive positive elastic restoring forces generated in high-shear throat regions, completely eliminating the need for negative energy densities. Keywords: Topological Conduits, Wormhole Stability, Viscoelastic Vacuum, Maxwell-Oldroyd-B Rheology, Emergent Topology, Exotic Matter Alternative.