Logarithmic-Spiral Tubular Wormholes Supported by Electromagnetic Fields and Non-Minimal Torsion Coupling in Einstein-Cartan Gravity

Description: This project presents an explicit model of traversable wormholes with a logarithmic-spiral tubular geometry, supported by electromagnetic fields and a non-minimal torsion coupling in the Einstein–Cartan framework. Departing from spherical symmetry, the construction employs the Frenet–Serret formalism to derive the full tube metric, including non-diagonal terms encoding intrinsic curvature and torsion. Key Results: A standard electromagnetic field, non-minimally coupled to torsion, generates an effective stress-energy tensor that locally violates the Null Energy Condition (NEC). The spiral geometry acts as a “geometric amplifier,” reducing the energy required to sustain the throat compared to spherical models. An analytical solution demonstrates that the throat can be maintained with finite curvature invariants and no event horizons. Keywords: wormholes, Einstein–Cartan gravity, torsion, logarithmic spiral geometry, NEC violation, electromagnetic fields, geometric amplification.