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

TL;DR

This paper investigates a helical spacetime with unique geometric and physical properties, revealing negative energy regions, stable photon orbits, and torsion-influenced wave modes, with implications for gravitational and condensed matter systems.

Contribution

It provides an exact solution for a helical spacetime with negative energy density and explores its optical and physical properties, linking gravity and condensed matter analogues.

Findings

Negative energy density near the axis

Stable photon orbits identified

Torsion affects wave and particle trajectories

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.