Helically twisted spacetime: Study of geometric and wave optics, and physical analysis

We analyse a stationary, cylindrically symmetric spacetime endowed with an intrinsic helical twist, ds2=−dt2+dr2+r2dϕ2+(dz+ωrdϕ)2. Solving the Einstein equations exactly yields an anisotropic energy–momentum tensor whose density is negative and decays as r−2, thus violating the weak energy condition near the axis. Three notable features emerge: (i) axis-centred negative energy; (ii) unequal transverse stresses; (iii) a torsional momentum flux Tϕz∝ω3/r. We identify stable photon orbits and deflection angle, fully helical geodesics, and torsion-controlled wave optics modes, suggesting laboratory analogues in twisted liquid-crystal and photonic systems. The coupling between the torsion parameter ω and other physical parameters leads to significant effects, altering the motion along the positive or negative z-axis. These results make the twisted helical metric a useful test bed for studying the interplay of curvature, torsion, and matter in both gravitational and condensed-matter contexts.