Characterization of exotic matter in PT-symmetric wormholes

Abstract: In our previous work [H. Zejli, Int. J. Mod. Phys. D 34, 2550052 (2025), arXiv:2508.00035], we introduced a PT-symmetric wormhole model based on a bimetric geometry, capable of generating closed timelike curves (CTCs). In this paper, we extend the analysis to the null hypersurface at the throat of this modified Einstein-Rosen bridge, where two regular Eddington-Finkelstein metrics render the geometry traversable. Using the Barrabes--Israel formalism in Poisson's reformulation, we evaluate the null shell's surface stress-energy tensor $S^{αβ}$ from the jump of the transverse curvature, revealing a violation of the null energy condition: a lightlike membrane of exotic matter with negative surface energy density and positive tangential pressure. This exotic fluid acts as a repulsive source stabilizing the throat, ensuring consistency with the Einstein field equations, including conservation laws on the shell. Beyond the local characterization, we outline potential observational signatures: (i) gravitational-wave echoes from the photon-sphere cavity; (ii) horizon-scale imaging with duplicated and through-throat photon rings, and non-Kerr asymmetries; (iii) quantum effects such as PT-induced frequency pairing with possible QNM doublets and partial suppression of vacuum flux at the throat; and (iv) a relic cosmological population yielding an effective $Λ_{\mathrm{eff}}$ and seeding voids. Compared with timelike thin-shell constructions, our approach is based on a null junction interpreted as a lightlike membrane, combined with PT symmetry, providing a distinct route to traversability and clarifying the conditions under which CTCs can arise in a self-consistent framework.