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arXiv · 2506.23291

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

Edilberto O. Silva·Frankbelson dos S. Azevedo·Faizuddin Ahmed
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Abstract

We analyse a stationary, cylindrically symmetric spacetime endowed with an intrinsic helical twist, $ds^{2} = -dt^{2} + dr^{2} + r^{2} d\phi^{2} + (dz + \omega\, r\,d\phi)^{2}$. 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 $T_{\phi z}\omega^{3}/r$. 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 $\omega$ 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.

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Edilberto O. Silva, Frankbelson dos S. Azevedo, Faizuddin Ahmed. 2025-06-29. Helically twisted spacetime: study of geometric and wave optics, and physical analysis. https://doi.org/10.1016/j.physletb.2025.139944

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