We consider stationary, cylindrically symmetric configurations in general relativity and formulate necessary conditions for the existence of rotating cylindrical wormholes. It is shown that in a comoving reference frame the rotational part of the gravitational field is separated from its static part and forms an effective stress-energy tensor with exotic properties, which favors the existence of wormhole throats. Exact vacuum and scalar-vacuum solutions (with a massless scalar) are considered as examples, and it turns out that even vacuum solutions can be of wormhole nature. However, solutions obtainable in this manner cannot have well-behaved asymptotic regions, which excludes the existence of wormhole entrances appearing as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions by the cut-andpaste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space at some surfaces Σ − and Σ + . It is shown, however, that if we describe the throat region with vacuum or scalar-vacuum solutions, one or both thin shells appearing on Σ − and Σ + inevitably violate the null energy condition. In other words, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.

We consider the dynamics of a self-gravitating spinor field and a self-gravitating rotating perfect fluid. It is shown that both these matter distributions can induce a vortex field described by the curl 4-vector of a tetrad:l;m , where e (a) k are components of the tetrad. The energy-momentum tensor T ik (ω) of this field has been found and shown to violate the strong and weak energy conditions which leads to possible formation of geometries with nontrivial topology like wormholes. The corresponding exact solutions to the equations of general relativity have been found. It is also shown that other vortex fields, e.g., the magnetic field, can also possess such properties.As we have shown earlier [1, 2], a self-gravitating Dirac spinor field with the Lagrangian

All known solutions to the Einstein equations describing rotating cylindrical wormholes lack asymptotic flatness in the radial directions and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, wormhole solutions are joined to flat asymptotic regions at some surfaces Σ − and Σ + . The whole configuration thus consists of three regions, the internal one containing a wormhole throat, and two flat external ones, considered in rotating reference frames. Using a special kind of anisotropic fluid respecting the Weak Energy Condition (WEC) as a source of gravity in the internal region, we show that the parameters of this configuration can be chosen in such a way that matter on both junction surfaces Σ − and Σ + also respects the WEC. Closed timelike curves are shown to be absent by construction in the whole configuration. It seems to be the first example of regular twice (radially) asymptotically flat wormholes without exotic matter and without closed timelike curves, obtained in general relativity.1 e-mail: kb20@yandex.ru are known in extensions of GR, such as the Einstein-Cartan theory [12,13], Einstein-Gauss-Bonnet gravity [14], brane worlds [15] and other multidimensional models [16], etc. We here prefer to adhere to GR as a theory well describing the macroscopic reality while the extensions more likely concern very large densities and/or curvatures. In GR there are phantom-free wormhole models with axial symmetry, such as the Zipoy [17] and superextremal Kerr vacuum solutions as well as solutions with scalar and electromagnetic fields [18,19]; in all of them, however, a disk that plays the role of a throat is bounded by a ring singularity whose existence is a kind of unpleasant price paid for the absence of exotic matter. Regular phantom-free wormholes in GR were found in [20,21], sourced by a nonlinear sigma model, but they are asymptotically NUT-AdS instead of the desired flatness. A phantom-free wormhole construction in [22] contains singularities and closed timelike curves. These shortcomings may be interpreted as manifestations of topological censorship.The above-mentioned results of [7] as well as topological censorship are not directly applicable arXiv:1807.03641v4 [gr-qc]

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We seek wormholes among rotating cylindrically symmetric configurations in general relativity. Exact wormhole solutions are presented with such sources of gravity as a massless scalar field, a cosmological constant, and a scalar field with an exponential potential. However, none of these solutions are asymptotically flat, which excludes the existence of wormhole entrances as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions using the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space-time at some surfaces $\Sigma_-$ and $\Sigma_+$. It is shown, however, that if the source of gravity in the throat region is a scalar field with an arbitrary potential, then one or both thin shells appearing on $\Sigma_-$ and $\Sigma_+$ inevitably violate the null energy condition. Thus, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.Comment: 10 pages, no figures. Submitted to Proc. of the 9th Alexander Friedmann International Seminar on Gravitation and Cosmolog