Behavior of a test gyroscope moving towards a rotating traversable wormhole

The geodesic structure of the Teo wormhole is briefly discussed and some observables are derived that promise to be of use in detecting a rotating traversable wormhole indirectly, if it does exist. We also deduce the exact Lense-Thirring (LT) precession frequency of a test gyroscope moving toward a rotating traversable Teo wormhole. The precession frequency diverges on the ergoregion, a behavior intimately related to and governed by the geometry of the ergoregion, analogous to the situation in a Kerr spacetime. Interestingly, it turns out that here the LT precession is inversely proportional to the angular momentum ($a$) of the wormhole along the pole and around it in the strong gravity regime, a behavior contrasting with its direct variation with $a$ in the case of other compact objects. In fact, divergence of LT precession inside the ergoregion can also be avoided if the gyro moves with a non-zero angular velocity in a certain range. As a result, the spin precession frequency of the gyro can be made finite throughout its whole path, even very close to the throat, during its travel to the wormhole. Furthermore, it is evident from our formulation that this spin precession not only arises due to curvature or rotation of the spacetime but also due to the non-zero angular velocity of the spin when it does not move along a geodesic in the strong gravity regime. If in the future, interstellar travel indeed becomes possible through a wormhole or at least in its vicinity, our results would prove useful in determining the behavior of a test gyroscope which is known to serve as a fundamental navigation device.