We analyze the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations. It is shown that the solution has a naked ring singularity which is unreachable to null geodesics falling freely from the outside. Similarly to Roger Penrose's cosmic censorship, that states that all naked singularities in the Universe must be protected by event horizons, here we conjecture from our results that a naked singularity can also be fully protected by the intrinsic properties of a wormhole's throat.

We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-Dilaton-Axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions Sp(4, ) ∼ O(5). We find solutions of the EMDA field equations for the one and two dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find space-times that generalise the Schwarzschild solution with dilaton, axion and electromagnetic fields.

In this work we study 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, other wise it is regular everywhere. The mean feature of this wormhole is that the mouth of the throat lie on a sphere of the same radius as the ring singularity an avoids any observer to see or to reach the singularity, it behaves like an anti-horizon. 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. 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.PACS numbers: 98.62.Ai, 95.30.Sf

In this work we wonder if there is a way to generate a wormhole (WH) in nature using "normal" matter. In order to give a first answer to this question, we study a massless scalar field coupled to an electromagnetic one (dilatonic field) with an arbitrary coupling constant, as source of gravitation. We obtain an exact solution of the Einstein equations using this source that represents a magnetized rotating WH. This space-time has a naked ring singularity, probably untouchable as in [18], but otherwise regular. The WH throat lies on the disc bounded by the ring singularity, which keeps the throat open without requiring exotic matter, that means, satisfying all the energy conditions. After analyzing the geodesic motion and the tidal forces we find that a test particle can go through the WH without troubles.

In this proceedings we review a method for generating rotating wormhole solutions of the Einstein equations with ghost (phantom) matter. One of the solutions contains a ring singularity only on the south hemisphere. We analyze the geodesic motion around this solution and show that there is no geodesics touching the ring singularity of the wormhole in any way. This leads us to the famous Penrose's cosmic censorship conjecture.