Transmission and quasinormal modes of massive vector field in (2+1)-dimensional static wormhole in vacuum

Abstract

This investigation examines the behavior of a massive vector field in the context of a 2+1-dimensional static wormhole in vacuum, with a focus on both transmission characteristics and quasinormal modes (QNMs). Using the Duffin–Kemmer–Petiau (DKP) equation to describe the massive vector field, analytical expressions for the transmission coefficients are derived, and the QNMs are identified as the complex poles of these coefficients. The analysis demonstrates that the transmission varies significantly with the angular momentum and throat and curvature radii of the wormhole, with $\ell =0$ modes exhibiting higher transmission rates. Regarding the QNMs, it was shown that for $\ell =0$, the system can transition between evanescent and propagative modes depending on the mass threshold of the vector field. However, for $\ell \ge 1$, the system, in addition to exhibiting long-lived modes when the mass is large, does not exhibit anomalous behavior in the decay rate for any overtone value. These findings provide insights into the response dynamics of static wormholes in vacuum under perturbations of massive vector fields, contributing to a more comprehensive understanding of exotic space-time geometries.