Optical and Dynamical Signatures of Padé Approximated Wormholes in $f(T)$ Gravity

Abstract

We construct traversable wormhole solutions in the linear teleparallel model $f(T) = αT + β$, adopting Padé approximants of order [1/0] and [0/1] as shape functions together with the redshift function $Φ(r) = -M/r$, and derive the corresponding source terms from the modified field equations. We assess the physical viability of both configurations through the energy conditions, Tolman--Oppenheimer--Volkoff equilibrium, the volume integral quantifier, thin-shell junction matching to an exterior Schwarzschild vacuum, embedding diagrams, proper radial distance, the gravitational energy and the active mass. We then examine the observational signatures of each geometry by analysing equatorial null geodesics and the photon-sphere structure, computing shadow maps and radial intensity profiles, ray-tracing relativistic images of a geometrically thin accretion disc, and integrating timelike rosette orbits. Finally, we study the dynamical stability of both wormholes through a third-order WKB quasinormal-mode analysis across scalar, electromagnetic, and axial gravitational perturbations, cross-checked against time-domain evolution and the eikonal photon-sphere correspondence, and examine the parameter dependence of the mode spectrum together with the possibility of trapped-mode echoes.