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

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 $\hat{I}›$ 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 $\hat{I}›$ increases, since the magnitude of $3$-form decreases with $\hat{I}›$. 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 $\hat{I}›$ 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 $\hat{I}›$ is sufficiently large, precisely when NEC is weakly violated.

17 pages, 3 figures, reference added, updated to match the published version