Scalar-Field Wave Dynamics and Quasinormal Modes of the Teo Rotating Wormhole

TL;DR

This work analyzes scalar perturbations, quasinormal modes (QNMs), and wave-geometry coupling in the rotating Teo wormhole. By separating variables in the Klein–Gordon equation and transforming to a Schrödinger-type radial equation, it reveals a single, near-throat potential barrier shaped by frame dragging, producing damped QNMs whose frequencies and damping rates vary monotonically with the rotation parameter $a$. The study establishes an eikonal correspondence between QNMs and photon-ring properties while contrasting horizonless Teo wormholes with Kerr black holes, notably showing mode-splitting patterns that saturate due to throat reflection and the absence of horizon absorption. These results identify spectral signatures—such as one-sided mode-splitting and reduced damping variability—that could help distinguish rotating wormholes from rotating black holes in strong-field observations. The findings illuminate how rotation and boundary conditions jointly govern wave propagation in horizonless compact objects and set the stage for future explorations of time-domain evolution, broader wormhole families, and observational templates for gravitational-wave and electromagnetic signatures.

Abstract

We investigate scalar field perturbations of the rotating Teo wormhole. We also compute the quasinormal mode (QNM) spectrum using first order WKB approximation. After separation of variables, we obtain a Schroedinger type radial equation and a smooth barrier potential which is shaped by the localized frame-dragging effects of the wormhole throat. This barrier potential provides damped oscillatory modes for the range of spins that were examined. The QNM spectrum shows a coherent and monotonic dependence on rotation. As the spin increases, both the oscillating frequency of the scalar wave and its damping rate decrease, which indicates progressively longer lived modes in the absence of absorption due to a horizon. We have verified the correspondence in the Eikonal limit, by obtaining the radius of the photon ring, its orbital frequency, and the Lyaponov exponent. Next, we compared the Teo wormhole QNM with that of the Kerr black hole QNM to find that the Kerr QNM is dictated by absorption at the horizon and they also exhibit symmetric pro-grade retrograde mode splitting, whereas the Teo wormhole QNM shows a stronger, and spatially confined response to spin. The Teo wormhole also exhibit partial reflection at the throat and a very distinct one-sided mode splitting which rapidly saturates as the spin increases. Additionally, the rotating Teo wormhole allows an ergoregion with the possibility of frequency kinematics compatible with superradiance. Due to the absence of an event horizon or a dissipative boundary, there is no evidence of classical superradiant amplification that was seen in Kerr. The results we obtained clearly demonstrates how rotation and boundary conditions jointly shape wave propagation in horizonless compact objects. They also provide certain characteristic spectral signatures that can be used to distinguish rotating wormhole spacetimes from rotating black hole spacetimes.

Figures (13)

• Figure 1: Klein--Gordon effective potential $V_{\rm eff}(r)$ for several rotation parameters $a$. Larger $a$ increases the magnitude of the near-throat contribution $m\Omega(r)\propto a/r^{3}$, producing a steeper rise in the inner region. At large radii, frame dragging becomes negligible and all curves approach the asymptotic value $V_{\rm eff}\to\omega^{2}$. This potential is derived from the separated scalar wave equation and is distinct from the Schrödinger-form potential used in the WKB analysis.
• Figure 2: Klein--Gordon effective potential $V_{\rm eff}^{\rm (KG)}(r)$ for the rotating Teo wormhole, extended to $r=100$ to verify the correct asymptotic decay. The inset shows a zoom of the far--region behavior where $V_{\rm eff}^{\rm (KG)}(r)\rightarrow 0^{-}$. The vertical dashed red line marks the photon--ring radius $r_{\rm ph}$ obtained independently from the null circular--geodesic conditions. Although the KG potential does not determine $r_{\rm ph}$, its extremum lies close to the photon ring for the representative parameters shown here, reflecting the familiar eikonal correspondence between wave dynamics and unstable null orbits.
• Figure 3: Photon–ring radius $r_{\rm ph}$, angular frequency $|\Omega_{\rm ph}|$, and Lyapunov exponent $\lambda$ as functions of the rotation parameter $a$, computed entirely from the null circular–geodesic conditions. Increasing $a$ shifts the photon ring outward, lowers the orbital frequency, and reduces the instability of the orbit.
• Figure 4: Eikonal QNM correspondence for the Teo wormhole. The real part $\omega_R \simeq m|\Omega_{\rm ph}|$ (blue) and the damping rate $-\omega_I \simeq (n+\tfrac{1}{2})\lambda$ (orange) both decrease as the rotation parameter $a$ increases, reflecting the outward shift and reduced instability of the photon ring.
• Figure 5: Schrödinger-form effective potential $V_{\mathrm{eff}}^{(\mathrm{Schr})}(r)$ for scalar perturbations of the rotating Teo wormhole. The barrier peak (red point) marks the location $r_{\rm peak}$ at which the first-order WKB approximation is evaluated. The potential decays to zero at large radii, as required for an asymptotically flat scattering problem. The extracted WKB estimate $\omega_{\rm WKB}\approx 3.636 - 1.958\,i$ reflects a damped quasinormal mode arising from wave leakage through the near-throat barrier.