A Unified Energy-Stress-Vorticity Equivalence and the Morphological Bifurcation Index of Cosmic Structures

Building upon my previous models of topological strain in multiply-connected manifolds and viscous dark sector hydrodynamics, this paper proposes a unified mechanical formulation that extends the relativistic mass-energy equivalence . I synthesize topological stress thresholds with local fluid vorticity to derive a modified energy equation, , where global isotropic confining pressure , critical topological rupture stress , and 3D fluid vorticity jointly modulate mass-energy states. Furthermore, I introduce the dimensionless Morphological Bifurcation Index (), which dictates whether a cosmic entity conforms to spherical hydrostatic symmetry () or rotates into planar vortex structures (). This framework bridges continuum stress mechanics, general relativity, and dark sector dynamics into a single analytical model.