Continuum Shear Failure: Resolving Gravitational Singularities via Visco-Elastic Phase Transitions

The prediction of curvature singularities and the emergence of Cauchy horizons remain critical pathologies within the general theory of relativity. While recent semi-classical models suggest that angular momentum and quantum dissipation may prevent infinite density, these approaches continue to superimpose quantum fields over an idealised, frictionless geometric void. This paper resolves the endpoint of gravitational collapse by replacing the geometric vacuum with a fully parameterised, visco-elastic fluid continuum: The Quantum Vector Time Field (QVTF). By modelling black holes as extended macroscopic vortex-solitons rather than dimensionless points, we demonstrate that extreme gravitational compression is strictly governed by the thermo-mechanical yield limits of this fluid medium. We define a Criticality Ratio (𝜒𝑐) as the threshold at which the localised inward acoustic pressure gradient (|∇𝑃𝑇 𝐹|) overcomes the continuum’s effective dynamic viscosity (𝜂𝑇 𝐹) and centrifugal shear. Reaching this threshold induces Continuum Shear Failure, forcing a localised, first-order reverse phase transition that mechanically compacts the fluid into a hyper-rigid solid-state inclusion. Consequently, the singularity is mathematically and physically averted, replaced by a stabilised solid-state core bounded by an acoustic wake-shedding event horizon. Finally, we establish quantitative bounds anchored to the Tolman-Oppenheimer-Volkoff limit and predict distinct, falsifiable acoustic anomalies in the quasinormal ringdown modes of binary black hole mergers.