The sharpest result is a mismatch between the model’s appearance and its spectrum. Images for singular and regular black-hole cases differ only slightly, but modes with nonzero real parts in the axial gravitational spectrum vary substantially as the bounce parameter a changes. The authors describe the two patterns as possible complementary diagnostics, not as evidence from an observed object or measured signal.
One model, several geometries
Each result comes from a selected configuration in a parameterized mathematical model, not an empirical sample. The study varies the bounce parameter a, the cosmological parameter, the multipole number and the placement of the cosmological horizon.
The calculations examine three horizon separations: xCH = 1.1 xEH, xCH = 5 xEH and xCH = 20 xEH. Event-horizon cases have a ∈ [0, xEH), while horizonless cases have a ∈ (xEH, xCH).
For nonzero a, selected curvature invariants remain finite at the origin, and the family spans regular black-hole, extremal and traversable-wormhole configurations.
The horizon class changes with a: when a > xEH the model is horizonless and traversable-wormhole-like; when a < xEH it has two oppositely signed event horizons; at a = xEH it is described as a one-way wormhole with a throat horizon.
What changes in the images
To calculate what a static observer would see, the authors trace light paths and separate emission into direct, lensed and photon-ring orders. Transfer functions map emission locations to trajectory impact parameters, and the modeled circular photon orbit is unstable.
Across the black-hole cases, the reported images show only tiny differences between singular and regular geometries. Traversable-wormhole cases show differences in observed luminosity, while event-horizon presence matters more for these images than the presence or location of the cosmological horizon.
That optical result is conditional on the chosen intensity profile, observer location and parameter cases. The study does not provide measured shadow or photon-ring data.
The spectrum tells a different story
For the gravitational calculation, a pseudospectral method obtains the fundamental quasinormal mode and its overtones without an initial guess. These are the complex frequency patterns calculated for axial gravitational perturbations.
The spectrum separates into two families. Modes with nonzero real parts vary significantly with a, while purely imaginary modes remain almost unaffected.
Horizonless configurations add a further pattern: quasistationary modes are reported near xEH; near xCH, the spectrum approaches a Pöschl-Teller-like form, an approximate mathematical template used in the calculation; and one purely imaginary mode approaches zero near xCH.
The calculation covers selected horizon placements, multipoles, parameter ranges and axial perturbations. It therefore does not establish behavior in every perturbation sector, full nonlinear stability or whether future observations could distinguish the models.
Clues, not confirmation
The authors’ proposed division is clear: cosmological-horizon-dependent gravitational-wave frequencies and comparatively unchanged photon-ring substructure could provide different clues about the underlying geometry.
But the preprint offers conditional predictions from a parameterized model. It does not show that any observed astrophysical object is a regular black hole or a wormhole.
Paper data and sources
Original title: Analyzing Quasi-normal modes spectrum in asymptotically de Sitter black bounces and their optical appearance
Authors: G. Alencar, Albert Duran-Cabacés, A. Lima et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text