Topological Reconnection in General Relativity and Fluid Continua

This treatise establishes a formal duality between vortex filament reconnection in fluid continua and gravitational field line reconnection in General Relativity. Key pillars of the work: Solenoidal Dipolar Foundation: Replaces singular point-vortex approximations with fully divergence-free vorton dipoles. This eliminates artificial velocity blowups, preserves Kelvin circulation constraints, and guarantees that field lines remain smooth and continuous through the reconnection vertex. Resolution of the Symplectic Obstruction: Resolves the classical mathematical barrier that strictly forbids topology change in ideal, energy-conserving Hamiltonian fields. By incorporating open non-ideal dynamics—represented in fluids by effective viscosity and in gravity by dissipative energy loss to outgoing gravitational waves—field lines can legitimately tear, cross, and reconnect. Autonomous Core Scale and Singularity Capping: Replaces zero-radius singular sheets with a first-principles core scale dictated by relativistic speed-of-light constraints and turbulent cascade dynamics. This finite scale imposes an upper bound on the spacetime curvature scalar, preventing the formation of naked singularities during extreme compression. Exact Fluid-Spacetime Equivalence: Utilizes an exact metric inversion of moving-medium electrodynamics to demonstrate that physical fluid vorticity directly maps to gravitomagnetic curvature, proving that both systems follow identical topological transition rules.