Resonant transmission of scalar waves through rotating traversable wormholes ✦
We studied the propagation of a massless scalar field in the spacetime of a rotating traversable wormhole described by Teo-class solutions. The transmission coefficient (greybody factor) and absorption spectrum were computed numerically over a wide frequency range. The spectrum shows sharp peaks identified as Breit-Wigner resonances. These peaks arise from the temporary trapping of scalar modes in a potential well formed by barriers on both sides of the throat. Previously found in static wormholes, the resonances persist in rotating cases: for Teo solutions, rotation amplifies their amplitude. The results highlight the role of rotation in shaping the resonance effect and point to these features as characteristic signatures of wormhole geometry.
Context
Exotic compact objects, such as traversable wormholes, remained purely theoretical constructs until observational astrophysics reached the frontiers of strong gravity. Back then, Albert Einstein and Nathan Rosen considered a bridge connecting two sheets of spacetime, and the term itself was introduced by John Wheeler. A modern impetus was given by Kip Thorne and Michael Morris, who proposed the concept of a traversable wormhole. Such objects require exotic matter that violates energy conditions, echoing the phenomenon of dark energy — a mysterious substance causing the accelerated expansion of the Universe. With the advent of gravitational wave detection and images of black hole shadows, the question of their distinctive signatures has become relevant, especially given the almost universal rotation of astrophysical bodies. Rotation can stabilize a wormhole and modify field scattering, creating a unique 'spectral fingerprint' linked to gravitational redshift.
Methods
The study is based on solving the Klein-Gordon equation for a massless scalar field against the background metric of a rotating Teo-class wormhole. Using numerical simulation in Mathematica, the reflection and transmission coefficients were found. The equation was reduced to a Schrödinger-like form with an effective potential depending on spacetime curvature, the orbital and magnetic quantum numbers, and the angular rotational velocity. For analysis, transmission spectroscopy was used, constructing the greybody factor and the total absorption cross-section. The incident wave was set at an arbitrary angle to the rotation axis, allowing orientation effects to be taken into account.
Results
The results showed that in the static limit, the absorption spectrum exhibits only weak resonances due to the shallow potential well near the throat. However, when rotation is turned on, pronounced Breit-Wigner peaks appear, especially for counter-rotating modes (azimuthal quantum number m < 0). For example, for l=1, m=-1 at spin a=0.7, the resonance is observed at frequency ωM ≈ 0.22, and for the co-rotating mode (m=1) — at ωM ≈ 0.54 at the same spin. Rotation deepens the potential well, increasing the lifetime of quasi-bound states and the amplitude of resonances. A key difference from black holes is the absence of superradiance: in a wormhole, the incident wave is not amplified but only partially passes through the throat. As the incidence angle increases from the rotation axis, the resonant peaks strengthen, reaching a maximum at perpendicular incidence.
Implications
The obtained results mean that a rotating traversable wormhole has a distinct 'spectral fingerprint' — a set of resonant frequencies that could be detected by observing accreting matter. This opens the way to the astrophysical identification of wormholes, in particular via analysis of accretion disks, whose properties in the presence of a throat and absence of an event horizon may differ radically from standard disks around black holes. Moreover, the angular dependence of the absorption cross-section provides an additional observational test for probing spacetime geometry.
Future development
Further development of the topic involves constructing more realistic models of rotating wormholes from alternative metric classes, as well as accounting for the back-reaction of the scalar field on geometry. A key step will be computing long-lived quasinormal modes in the double-peak potential, which should correspond to the resonant frequencies. It can be expected that similar effects will also appear for electromagnetic radiation, allowing multi-wavelength spectroscopy methods to be applied to search for wormholes in data from next-generation telescopes such as the JWST.
Impact
These results will affect the interpretation of observations of black hole candidate objects, especially when constructing shadows and analyzing accretion spectra. They also stimulate the development of numerical methods in strong-field physics and may be tested by future gravitational wave detectors.
Next steps
Next steps include modeling radiation from an accretion disk around a rotating wormhole and comparison with data from the Event Horizon Telescope. It is also necessary to investigate the stability of the throat when accounting for the back-reaction of scalar fields.
Key open problems
The work is directly connected to the unresolved problem of identifying exotic compact objects and the nature of the event horizon. Resonant signatures may help answer the question: do black holes exist in the Universe, or their imitators without singularities?
🎯 The Breit-Wigner resonances detected in the wormhole spectrum are analogous to resonances in nuclear physics, where they describe excited states of atomic nuclei. Thus, the wormhole 'rings' like an atomic nucleus, but on the scale of spacetime.
🎬 The idea of a traversable wormhole gained widespread fame thanks to Carl Sagan's novel 'Contact' and the film 'Interstellar', where such objects are used for travel through spacetime.
Key numbers
- maximum spin considered: a = 0.9
- resonance frequency (l=1, m=-1, a=0.7): ωM ≈ 0.22
- resonance frequency (l=1, m=1, a=0.7): ωM ≈ 0.54
- maximum resonance effect: at perpendicular wave incidence to the rotation axis
- difference from black holes: absence of superradiance