Enhanced Frame-Dragging from Organized Momentum Sources in Linearized General Relativity

We present a class of stationary spacetime geometries with enhanced frame-dragging, sourced entirely by the gravitomagnetic sector of the stress-energy tensor (T⁰ⁱ), constructed within the framework of linearized General Relativity. The source is pressureless dust with organized rotational momentum distributed on a one-sheet hyperboloid of revolution, employing a counter-rotating Archimedes-screw geometry that converts rotational frame-dragging (h₀φ) into an axial gravitomagnetic component (h₀z). The solution satisfies all five classical energy conditions (NEC, WEC, SEC, DEC, and ANEC) by construction, requires no exotic matter, and exhibits non-trivial Riemann curvature within the linearized regime. A geometric amplification factor F_geo ≈ 3.8–6.1, arising from Anti-Venturi momentum concentration, paraboloid convergence, and double-screw co-construction, enhances the frame-dragging signal well beyond the bare Lense–Thirring prediction for an equivalent point source. For the 500 m reference configuration (R₀ = 100 m, M = 1.61 × 10⁸ kg, ω = 30 rad/s, J = 3.50 × 10¹³ kg·m²/s), the numerical solver yields a frame-dragging angular velocity Ω(0,0) ≈ 1.23 × 10⁻⁸ rad/s and a gravitomagnetic field B_g(0,0) ≈ 3.70 × 10⁻¹⁵ T. These predictions are independent of any amplification beyond the geometric enhancement and are directly testable: the predicted signal exceeds the sensitivity of existing ring laser gyroscopes (Canterbury UG-2) by three orders of magnitude (SNR ≈ 1,230) and existing atomic gyroscopes by one order of magnitude (SNR ≈ 20). We present a complete stability analysis (7 independent criteria confirming unconditional stability), second-order perturbative corrections establishing the domain of validity of the linearized approximation, and an analysis of the gauge-invariant topological content of the gravitomagnetic field, identifying a gravitational Aharonov–Bohm phase arising from the multiply-connected exterior topology. Keywords: frame-dragging, gravitomagnetism, linearized general relativity, stress-energy tensor, hyperboloid geometry, energy conditions, Lense–Thirring effect, source-first methodology, Aharonov–Bohm phase, experimental gravitation