Optical Appearances of Accreting Ellis-Bronnikov Wormholes Observed from Both Sides of Throats

Abstract: This study investigates the optical appearance of the Ellis-Bronnikov wormhole as viewed from both sides of its throat, under conditions of optically thick and thin accretion. By solving the geodesic equation, we derive the relationship between the impact parameter and the aiming distance of photons, and found that if the observer and the accretion disk are located on both sides of the throat, these two quantities are not equal. The optical image of the wormhole observed from the other side of the throat is obtained through the ray-tracing method. For optically thick accretion, increases in the parameter $n$ lead to an increase in the apparent size of the wormhole but a decrease in its brightness. For optically thin accretion, the image is similar to the internal and external inversion of the image observed from the other side. Furthermore, for optically thin accretion flows, the direct image does not block the emission from higher-order images, allowing radiation emitted from regions much closer to the event horizon to reach the observer. Our simulation results show that when the observer is on the $\mathcal{R}<sup>+$ side, EB wormholes with small $n$ can mimic the images taken by the EHT to some extent, while wormholes with large $n$ or with the observer on the $\mathcal{R}<sup>-$ side can be ruled out.

• The paper computes backward ray-traced images of accreting Ellis–Bronnikov wormholes from both asymptotic regions, showing that only the near-side region supports a standard geodesic accretion disk.
• The study finds that far-side observers see an inside-out inversion of disk morphology and brightness ordering, with the impact parameter rescaled substantially—for example, b ≈ 37.62d* for n = 2.
• The results suggest that small-n wormholes viewed from the near side can resemble black-hole images, while large-n models and all far-side configurations conflict with current EHT observations.

The optical appearance of accreting compact objects has become a central tool for testing strong-field gravity since the Event Horizon Telescope (EHT) resolved the shadows of M87* and Sagittarius A*. This paper extends the program of wormhole imaging by computing, via backward ray tracing, the optical appearance of the Ellis–Bronnikov (EB) wormhole — the original traversable wormhole solution of Ellis and Bronnikov (1973) — as seen by observers on both sides of the throat ($\mathcal{R}^+$ and $\mathcal{R}^-$), under both optically thick and optically thin accretion. The key methodological contribution is the demonstration that, for observers on the far side of the throat, the impact parameter $b$ and the aiming distance $d^*$ are related by $b = \lim_{r\to\pm\infty} d^*/f(r)$, so that for $n=2$, $b \approx 37.62\, d^*$ in $\mathcal{R}^-$. This relation, derived in an appendix for general static spherically symmetric spacetimes, implies that images seen from $\mathcal{R}^-$ are strongly distorted relative to their apparent source geometry.

Spacetime structure and geodesics

The EB metric depends on two parameters $n > m$, with $\mathcal{R}^-$0 playing the role of the mass (set to $\mathcal{R}^-$1 throughout). Both asymptotic regions are flat, but the effective speed of light differs between them by a factor $\mathcal{R}^-$2; as $\mathcal{R}^-$3 increases the two sides become increasingly symmetric and flat. The throat sits at $\mathcal{R}^-$4, and the photon circular orbit lies at $\mathcal{R}^-$5 with a critical impact parameter

$\mathcal{R}^-$6

which decreases with $\mathcal{R}^-$7. The effective potential has a single peak at $\mathcal{R}^-$8, and the classification of unbound photon orbits differs qualitatively between the two sides: photons from $\mathcal{R}^-$9 with energy below the throat value $b$0 cannot even reach the throat, whereas all photons from $b$1 with sufficient energy cross it and never return.

The timelike analysis yields a physically decisive result: radial free fall is attractive on the $b$2 side but repulsive on the $b$3 side, so a standard accretion disk can only form in $b$4. The innermost stable circular orbit is $b$5, which grows monotonically with $b$6 — a fact that drives the imaging results below. This also means that any $b$7 observer is viewing a disk located entirely on the far side of the throat, which is precisely the configuration that produces the paper's most distinctive signatures.

Optically thick accretion

Using Luminet's ray-tracing formalism with the Page–Thorne flux profile, corrected for gravitational redshift and Doppler boosting, the authors find that for an observer in $b$8 the direct image of the EB wormhole is nearly indistinguishable from a Schwarzschild black hole; only the secondary image is slightly smaller, with the discrepancy growing with $b$9. The observed flux, however, is systematically dimmer than the black hole case and decreases with increasing $d^*$0, which the authors attribute to the growing $d^*$1 and the corresponding drop in disk angular velocity.

For the observer in $d^*$2, the image morphology changes qualitatively. Because inner disk radii are geometrically closer to the observer through the throat, the inner edge of the disk appears at the outer edge of the image: the radiative flux vanishes at the outermost boundary of the direct image rather than the innermost. This inside-out inversion is the paper's central observational claim. The authors also note that images in this configuration do not represent the true disk size, since the $d^*$3–$d^*$4 relation rescales the image by a factor of order $d^*$5 for moderate $d^*$6.

Optically thin accretion

Following the Gralla–Holz–Wald classification, the authors separate the direct image, lensing ring, and photon ring by the orbital number $d^*$7. A structural difference emerges between the two observer locations: in Case 2 ($d^*$8 observer), the impact parameter ranges are bounded above by $d^*$9, since photons must surmount the effective potential peak to reach the observer. Two toy emission functions are used — $b = \lim_{r\to\pm\infty} d^*/f(r)$0, decaying steeply from $b = \lim_{r\to\pm\infty} d^*/f(r)$1, and $b = \lim_{r\to\pm\infty} d^*/f(r)$2, decaying slowly from the photon sphere. The results reproduce and extend Huang et al. (2023): for an $b = \lim_{r\to\pm\infty} d^*/f(r)$3 observer, the radial ordering of direct image, lensing ring, and photon ring is inverted, and the flux gradient reverses direction relative to the $b = \lim_{r\to\pm\infty} d^*/f(r)$4 case. Unlike the optically thick case, the direct image does not occlude higher-order images, so radiation from radii well inside the ISCO — much closer to the throat — can reach the observer. The authors acknowledge that these emission models are toy models, valid for locating image components but not for realistic spectral predictions.

Constraints from EHT observations

The paper draws a direct, falsifiable conclusion: for an $b = \lim_{r\to\pm\infty} d^*/f(r)$5 observer, small-$b = \lim_{r\to\pm\infty} d^*/f(r)$6 EB wormholes can mimic the EHT images of M87* and Sgr A* to some extent, whereas wormholes with large $b = \lim_{r\to\pm\infty} d^*/f(r)$7 — whose enlarged $b = \lim_{r\to\pm\infty} d^*/f(r)$8 produces a shadow region significantly larger than a black hole's — and all configurations with the observer in $b = \lim_{r\to\pm\infty} d^*/f(r)$9 can be ruled out against current EHT data. The authors also note that the optical depth of the M87* flow is itself debated (optically thick at 86 GHz but thin at 230 GHz), so the distinction between the thick- and thin-accretion signatures developed here may be resolvable by the next-generation EHT's broader frequency coverage.

Limitations and open questions

Several caveats bound these results. The emission functions for the optically thin case are explicitly toy models, and the optically thick treatment assumes a geometrically thin, standard Page–Thorne disk on the equatorial plane; no magnetized or thick (toroidal) flows are considered. The claim that accretion disks form only on the $n=2$0 side rests on the geodesic repulsion in $n=2$1 and would need revisiting for self-gravitating or non-geodesic flows. The stability of the EB solution and the physical origin of the exotic matter supporting it remain open, and the analysis is restricted to static, spherically symmetric spacetimes — rotating generalizations, which would be required for quantitative comparison with EHT ring asymmetries, are left unaddressed.

Conclusion

This paper completes the program of EB wormhole imaging by covering both observer locations and both optical-depth regimes within a single ray-tracing framework. Its principal results are the $n=2$2–$n=2$3 relation for cross-throat observation, the demonstration that the far-side image is an inside-out inversion of the near-side image in both flux ordering and morphology, and the resulting exclusion of large-$n=2$4 wormholes and $n=2$5-side observers by existing EHT imagery. The inverted brightness profile is proposed as an observational fingerprint for wormholes, contingent on future instruments achieving the angular resolution and frequency coverage needed to test it.