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 work we present an analytical proof of cosmic censorship in a Kerr-like phantom wormhole (WH) which contains a singularity that is not protected by an event horizon. We show that the naked singularity of this space-time is causally disconnected from the universe. To do so, we consider a slowly rotating limit and by means of the Hamilton-Jacobi theory separate the Hamiltonian of the geodesics into two polynomials. During this process we find a fourth conserved quantity. After examining the properties of these polynomials we conclude that the ring singularity is untouchable by any observer traveling in a geodesic of this space-time. We also derive the conditions on the four constants of motion that are necessary for a traveler to go back and forth both universes connected through the WH, and then compare its structure to that of a negative mass Kerr black hole.

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In this work we study the local behavior of geodesics in the neighborhood of a curvature singularity contained in stationary and axially symmetric space–times. Apart from these properties, the metrics we shall focus on will also be required to admit a quadratic first integral for their geodesics. In particular, we search for the conditions on the geometry of the space–time for which null and time-like geodesics can reach the singularity. These conditions are determined by the equations of motion of a freely-falling particle. We also analyze the possible existence of geodesics that do not become incomplete when encountering the singularity in their path. The results are stated as criteria that depend on the inverse metric tensor along with conserved quantities such as energy and angular momentum. As an example, the derived criteria are applied to the Plebański–Demiański class of space–times. Lastly, we propose a line element that describes a wormhole whose curvature singularities are, according to our results, inaccessible to causal geodesics.