Traversable Wormhole in Einstein 3-Form Theory With Self-Interacting Potential

TL;DR

This paper numerically constructs a symmetric traversable wormhole supported by a massive 3-form field with a self-interaction potential, analyzing its properties, stability, and potential as a black hole mimicker.

Contribution

It introduces a new class of symmetric wormhole solutions in Einstein gravity with a self-interacting 3-form field, exploring their physical characteristics and observational signatures.

Findings

Wormholes have a single throat and are regular and asymptotically flat.

Mass and throat size increase with the self-interaction coefficient b3.

Wormholes can mimic black hole shadows, especially at large b3.

Abstract

We numerically construct 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. 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 $\Lambda$ 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 $\Lambda$ increases, since the magnitude of $3$-form decreases with $\Lambda$. In addition, we investigate the geodesics of particles moving around the wormhole. The unstable photon orbit is located at the throat. We also find 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 $\Lambda$ acquires a large value. The behavior of the innermost stable circular orbit around this wormhole is also discussed. The results of this paper hint toward the possibility that the 3-form wormholes could be potential black hole mimickers, as long as $\Lambda$ is sufficiently large, precisely when NEC is weakly violated.