Mariam Bouhmadi-Lopez and colleagues have constructed a symmetric wormhole solution in General Relativity (GR), which is supported by a 3-form field with a potential that contains a quartic self-interaction term. They hint towards the possibility that, the 3-form wormholes could be potential black hole mimickers, as long as the coefficient of the quartic self-interaction term (Λ) is sufficiently large, precisely when NEC is weakly violated. Their study recently appeared in *Arxiv*.

General Relativity (GR) is a well-tested theory, so it would be interesting to find traversable wormhole solutions in GR with “physically reasonable” matter field to support the throat. Such a matter field should preferably possess a correct sign for its kinetic energy though necessarily still violate some energy conditions. It would be even better if such a matter field is in some sense natural (e.g., it can also be applied to explain cosmological puzzles such as the accelerated expansion of the Universe). One natural candidate is the 3-form field which is ubiquitous to string theory within a cosmological framework and beyond.

Now, Mariam Bouhmadi-Lopez and colleagues numerically constructed a symmetric wormhole solution in pure Einstein gravity supported by a massive 3-form field with a potential that contains a quartic self-interaction term.

They found that, the wormhole spacetimes have only a single throat and they are everywhere regular and asymptotically flat. Furthermore, their mass and throat circumference increase almost linearly as the coefficient of the quartic self-interaction term Λ increases.

The amount of violation of the null energy condition (NEC) is proportional to the magnitude of 3-form, thus the NEC is less violated as Λ increases, since the magnitude of 3-form decreases with Λ.

In addition, they have investigated the geodesic equations for null particles and timelike particles moving around the wormhole. It is found that the unstable photon sphere/orbit, on which photons can undergo circular motions around the wormhole, is exactly at the wormhole throat.

In addition, they have investigated the geodesics of particles moving around the wormhole and found that the unstable photon orbit is located at the throat. They also found that the wormhole can cast a shadow whose apparent size is smaller than that cast by the Schwarzschild black hole, but reduces to it when Λ acquires a large value.

Moreover, they also discussed the behavior of the innermost stable circular orbit (ISCO) around this wormhole and found that the radius of ISCO deviates from the Schwarzschild counterpart when Λ is small, but reduces to it for a larger Λ. Thus, their wormholes can be a black hole mimicker when Λ is large, precisely when NEC is less violated.

“Of course, most astrophysical black holes rotate, so it remains to be seen if this mimicry still holds when rotation is considered.”

— authors of the study.

“Future investigation will look into the radial perturbation on the background metric and the form field to check stability, among other considerations. Indeed, the wormhole solutions supported by the complex phantom scalar field are found to be unstable against linear perturbations. It would be interesting to check whether our wormholes suffer from the same instability, and if so, for which range of Λ.”, they concluded.

**Reference***: Mariam Bouhmadi-López, Che-Yu Chen, Xiao Yan Chew, Yen Chin Ong, Dong-han Yeom, “Traversable Wormhole in Einstein 3-Form Theory With Self-Interacting Potential”, Arxiv, pp. 1-12, 2021. **arXiv:2108.07302*

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