Potentially observable cylindrical wormholes without exotic matter in general relativity

Abstract

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]

Cylindrical systems in general relativity

“…So, there is hope to obtain phantom-free wormholes, asymptotically flat in the radial direction. Among numerous known cylindrical wormhole solutions in GR (see, among others, [66,70,[78][79][80][81] and references therein) many are phantom-free but none are asymptotically flat, for the same reason for which the LC vacuum solution is only asymptotically flat if it is completely flat, that is, only when the entire spacetime is Minkowiski. To solve the problem, the following construction was suggested [78]: a central wormhole region with a throat, surrounded on both sides by Minkowski regions, matched through thin cylindrical shells Σ − and Σ + .…”

Rotating Cylinders with Anisotropic Fluids in General Relativity

“…A separate problem is to find such models where matter in the central region and on its both boundaries satisfies the Weak and Null Energy Conditions. These issues are beyond the scope of the present paper, for details see [6,7,26,27,34].…”

“…This problem is ignored in many studies, in which static cylindrical solutions are matched on some surfaces with a Levi-Civita exterior, and stationary ones with a Lewis exterior. This problem was discussed for wormhole models in [6,7,26,34], where, following the suggestion of [6], wormhole space-times were constructed with three regions: a central one containing a throat and two external Minkowski regions matched to this central one at some cylinders Σ − and Σ + . These surfaces inevitably contained some densities and pressures calculated from jumps of K ab across them.…”

“…Our purpose here is to present a general method of solving the Einstein equations using the fact that in stationary cylindrically symmetric space-times the Ricci and Einstein tensors split into static and rotational parts [6] and employing the harmonic radial coordinate, first applied to static cylindrical systems in [24]. This leads to reproducing some known solutions and obtaining new ones which can be applied to describe configurations with a regular symmetry axis and those where such an axis is absent (cylindrical wormholes [6,7,[25][26][27]. A thorough analysis of numerous systems of interest is postponed for the future, here we only briefly consider some examples.…”

Wormhole as a possible accelerator of high-energy cosmic-ray particles

“…Then the geometry acquires cylindrical configuration. In particular, in a series of papers [16][17][18][19] static and station- * Electronic address: ka98@mail.ru † Electronic address: sep 22.12.79@inbox.ru ary cylindrical wormhole solutions were found and it was demonstrated that asymptotically flat wormhole configurations do not require exotic matter violating the weak energy condition. Primordial wormholes may initially capture some electric and magnetic lines of force.…”