Multi-photon ring structure of reflection-asymmetric traversable thin-shell wormholes

TL;DR

The paper investigates how reflection-asymmetric traversable thin-shell wormholes, realized in Palatini f(R) gravity, imprint distinctive optical signatures on accretion-disk images. By matching two RN spacetimes at a throat and performing backward ray-tracing, the authors reveal two photon spheres and novel multi-photon rings arising from light crossing the throat, with the two-disk configuration producing many brighter rings and a substantially reduced shadow. These features differ from canonical black hole images and provide potential observational discriminators for ultra-compact objects using high-resolution VLBI, though practical detectability depends on redshift effects and instrument capabilities. The work underscores the potential of imaging to test alternative gravity solutions and horizonless compact objects beyond GR black holes.

Abstract

We consider the observational signatures of thin accretion disks around a reflection-asymmetric traversable thin-shell wormhole. This wormhole, built in the framework of Palatini $f(R)$ gravity coupled to a Maxwell field using a junction conditions formalism, lacks horizons but features photon spheres on each side of the throat, described by different effective potentials and at different locations. This fact allows a portion of the light rays arriving to the observer's screen on one side of the throat to have explored a part of the space-time on the other side, bringing information about the geometry gathered there. In this setting we simulate the optical appearance of such an asymmetric wormhole when illuminated by thin accretion disks, investigating scenarios with either one or two (on each side of the throat) disks, revealing a rich multi-photon ring structure due to light crossing the throat, and a strong reduction in the size of the central brightness depression region. These new rings are more numerous and far more luminous in the two-disk case than in the single-disk case, and the shadow's size reduction far more acute, making a neat distinction as compared to canonical black hole images. These results highlight the potential of high-resolution imaging in providing smoking guns for the existence of ultra-compact objects distinct from black holes via their multi-ring structure.

Figures (8)

• Figure 1: Effective potential $V_{eff}(x)$ as given by the union of the two potentials of Eq.(\ref{['eq:effpot']}) for the asymmetric wormhole according to the parameters set in Sec. \ref{['sec:asym']}. Both parts of the potential meet at the throat (yellow dashed line). The potential has two maxima: one in $\mathcal{M}_-$ (magenta dashed line), and one in $\mathcal{M}_+$ (green dashed line). We consider observers located on the right-hand side of this figure, which are the only ones capable of seeing the multi-photon ring structure.
• Figure 2: Trajectories of individual light rays in asymmetric traversable thin-shell wormholes for four picks of impact parameters: $b=b_c^+ + 0.0083$ (top left), $b=b_c^+ -0.0775$ (top right), $b=b_c^-+0.4$ (bottom left), and $b=b_c^-+0.005$ (bottom right), corresponding to the model parameters and units discussed in Sec. \ref{['sec:asym']}. Red curves correspond to ingoing trajectories on $\mathcal{M}_+$; blue curves to outgoing trajectories in $\mathcal{M}_-$; orange curves to ingoing trajectories in $\mathcal{M}_-$; and purple curves to outgoing trajectories in $\mathcal{M}_+$. The dashed black circle corresponds to the location of the wormhole throat, while the dashed green (yellow) circle corresponds to the location of the photon sphere on $\mathcal{M}_+$($\mathcal{M}_-$). Note that, the closer the impact parameter to $b_c^+$ ($b_c^-$) the larger the number of half-orbits on $\mathcal{M}_+$($\mathcal{M}_-$).
• Figure 3: Ray-tracing of two null geodesics with $b\approx b_c^\pm$ (blue and red), each approaching the corresponding photon sphere on the $\mathcal{M}_+$ and $\mathcal{M}_-$, respectively. On their path, each photon performs an arbitrary large number of half-turns.
• Figure 4: Ray-tracing for $b_c^+\leq b \leq 10$ (left), $b_c^-\leq b \leq b_c^+$ (middle), $0\leq b \leq b_c^-$ (right), representing the three possible behaviours of light rays according to the regions of the full manifold $\mathcal{M}$ they explore. Blue (red) curves correspond to trajectories on $\mathcal{M}_+$ ($\mathcal{M}_-$), while the wormhole throat corresponds to the central circle.
• Figure 5: Transfer function $r=r_n(b)$ as a function of the impact parameter. The left image corresponds to a Reissner-Nordström black hole, the middle image to an asymmetric wormhole with a single accretion disk, and the right image to the two-accretion disks case. In the two wormhole cases we see the presence of eight curves corresponding to the $n=0,1,2,3,4,5,6,7$ contributions to the image.