Miranda and colleagues in their paper, studied a Kerr-like wormhole with phantom matter as source. It has three parameters: mass, angular momentum and scalar field charge. This wormhole has a naked ring singularity (very similar to kerr black hole), otherwise it is regular everywhere (except on ring) (please refer note below if you don’t know about ring singularity). It has also a gauge parameter which determine the radius of the throat and a naked ring singularity, exactly the same one as the Kerr solution.
The mean feature of this wormhole is that throat is found outside of the ring singularity, the mouth of the throat lie on a sphere of the same radius as the ring singularity around the wormhole, this avoids any observer to see or to reach the singularity, it behaves like an anti-horizon.
They analyzed the geodesics of the wormhole and showed that the null polar geodesics/light-rays, that means, geodesics going through the polar line are regular, an observer can go through the throat if the observer trajectory remains on the polar geodesics and contains an energy bigger than 1/2f, for any values of the free parameters. On this trajectory the tidal forces are very small, therefore this wormhole is traversable. For any other angle the mouth of the wormhole lie on the sphere, but close to the equator, the effect of the wormhole is to repel the test particles. On the equator, the repulsion is infinity and nothing can reach the singularity, even the light is repealed by the wormhole.
“We analyse the geodesics of the wormhole and find that an observer can go through the geodesics without troubles, but the equator presents an infinity potential barrier which avoids to reach the throat.”— told Miranda, first author of the study
Thus, the sphere of the same radius as the ring singularity has an effect contrary to the horizon of a black hole, namely, an observer can reach the sphere, goes thought the throat, but this sphere avoids the traveller to observe or to reach the singularity. Of course, the traveller can come back to its original world without much troubles.
“From an analysis of the Riemann tensor we obtain that the tidal forces permits the wormhole to be traversable for an observer like a human being.”— told Miranda, first author of the study
Note: Ring singularity: A ring singularity is the gravitational singularity of a rotating kerr black hole/ wormhole shaped like a ring (as shown in fig below).
Reference: Miranda, G., Matos, T. & García, N.M. Kerr-like phantom wormhole. Gen Relativ Gravit 46, 1613 (2014). https://link.springer.com/article/10.1007/s10714-013-1613-y https://doi.org/10.1007/s10714-013-1613-y
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