Long-Throat Wormholes: How to Distinguish Them from Black Holes by Their Images ✦
Observational signatures — shadow, throat silhouette, and thin accretion disk image — have been studied for a family of static, spherically symmetric wormholes with an arbitrary throat profile. Expressions for the shadow radius, throat silhouette radius, and photon energy shift were derived in the general static spherically symmetric case. The resulting formulas were applied to a specific metric with three free parameters: throat radius a, throat length λ, and parameter u0 controlling the depth of the gravitational well. The shadow and silhouette radii were computed numerically as functions of the parameters, accretion disk images were generated for three representative parameter sets, and comparisons were made with the Schwarzschild black hole. It is shown that there exist parameter combinations for which the wormhole's shadow and throat silhouette coincide with those of a black hole of the same mass. Nevertheless, the accretion disk images are fundamentally different: in the wormhole, the Doppler effect dominates over gravitational redshift, making its image noticeably brighter.
Context
The search for astrophysical wormholes has intensified thanks to advances in observations of supermassive compact objects. The Event Horizon Telescope collaboration captured the first images of black hole candidates, ushering in an era of testing strong gravity. While these observations are consistent with theory, they do not rule out alternatives like wormholes, whose gravitational lenses and shadows can mimic black holes.
Methods
Based on a general parameterization of a static spherically symmetric metric with an arbitrary throat profile, analytical expressions were derived for the shadow radius, throat silhouette, and photon energy shift. For a specific model with parameters a, λ, and u0, geodesic equations were solved numerically, and embedding diagrams and accretion disk images were constructed. Comparison was made with the Schwarzschild black hole—the classic solution obtained by Karl Schwarzschild.
Results
It was found that there exist parameter sets a, λ, and u0 for which the shadow and throat silhouette radii of a wormhole exactly match those of a Schwarzschild black hole of equal mass. However, the accretion disk images differ dramatically: in a wormhole, the Doppler effect dominates over gravitational redshift. As a result, the wormhole disk appears much brighter—the maximum energy shift reaches 1.45 versus 0.74 for a black hole.
Implications
Joint analysis of the dark spot size and energy shift distribution provides a reliable observational tool to distinguish wormholes from black holes, paving the way for empirical testing of alternative gravity theories.
Future development
Future work includes extending the model to rotating wormholes, incorporating more realistic accretion models, and accounting for polarization of radiation for direct comparison with Event Horizon Telescope data.
Impact
The results will directly impact observational astrophysics of compact objects, gravitational lensing methods, and tests of general relativity.
Next steps
The next step involves simulating images for specific candidates like M87* and Sgr A*, incorporating the latest polarization data from the EHT collaboration.
Key open problems
This work is directly connected to the fundamental problem of identifying the true nature of supermassive compact objects and the search for exotic solutions of Einstein's equations alternative to black holes.
🎯 The term 'wormhole' was coined by John Wheeler in 1957, and the idea of using them for interstellar travel was popularized by Kip Thorne and Michael Morris in 1988.
🎬 In the movie 'Interstellar', a traversable wormhole serves as a portal to another galaxy, artistically echoing the theoretical possibility of travel through such objects.
Key numbers
- Schwarzschild black hole shadow: 5.196m
- Black hole horizon silhouette: 4.457m
- Max energy shift for wormhole (λ=1, u0=1): 1.45
- Max energy shift for black hole: 0.74
- Throat radius in wormhole model: 2m