Closed timelike geodesics in a gas of cosmic strings

Grøn, Øyvind; Johannesen, Steinar

doi:10.1088/1367-2630/10/10/103025

Cited by 21 publications

(24 citation statements)

References 19 publications

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“…Since the conditions (36) and (37) manifestly hold if (38) does, we conclude that there is a significant range in the parameter space (x 0 , y ) in which our wormhole model completely satisfies the WEC.…”

Section: Potentially Observable Modelsmentioning

confidence: 77%

“…A question of interest is whether the space-time described by this solution contains closed timelike curves (CTCs) that lead to causality violation. In the metric (1) such curves emerge if and only if g 33 > 0 (see, e.g., [37]), in which case the closed coordinate lines of the azimuthal angle ϕ are timelike. Consider the behavior of g 33 for the symmetric branch of the above solution, to be used in what follows.…”

Section: Wormhole Solution With An Anisotropic Fluidmentioning

confidence: 99%

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Potentially observable cylindrical wormholes without exotic matter in general relativity

Бронников

Krechet

2019

Phys. Rev. D

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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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Section: Potentially Observable Modelsmentioning

confidence: 77%

Section: Wormhole Solution With An Anisotropic Fluidmentioning

confidence: 99%

Potentially observable cylindrical wormholes without exotic matter in general relativity

Бронников

Krechet

2019

Phys. Rev. D

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“…Bonnor and Steadman [25] have shown that a spacetime with two spinning particles, under special circumstances, allow for the existence of CTGs. A class of solutions of Einstein's field equations with CTGs representing spacetime outside a spinning cosmic string surrounded by a region of finite radial extension with vacuum energy and a gas of strings [26] have been recently found. Other examples are a cylindrically symmetric spacetime [27] which admit CTGs everywhere outside an axis and a vacuum spacetime with CNGs found quite recently [28].…”

Section: Introductionmentioning

confidence: 99%

Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

Sarma¹,

Ahmed²,

Patgiri³

2016

Advances in High Energy Physics

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We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature singularity. The spacetime is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the spacetime also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.

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“…Thus when r 0 > 6 m, the constant ω is real and the solution (14) shows the typical behavior for stability, i.e., vibrational modes untangled with translational ones that can be eliminated by a suitable choice of the initial conditions.…”

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confidence: 99%

Spinning Strings, Black Holes and Stable Closed Timelike Geodesics

Rosa

Letelier

2009

Int J Theor Phys

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The existence and stability under linear perturbation of closed timelike curves in the spacetime associated to Schwarzschild black hole pierced by a spinning string are studied. Due to the superposition of the black hole, we find that the spinning string spacetime is deformed in such a way to allow the existence of closed timelike geodesics. The existance of closed timelike curves (CTCs) in the Gödel universe and other apacetimes is a worrying fact since these curves show a clear violation of causality. In some cases these CTCs can be disregarded by energy considerations. Their existance requires an external force acting along the whole CTC, process that may consume a great amount of energy. The energy needed to travel along a CTC in Gödel's universe is computed in [1]. When the external force is null the energy needed to travel is also null. Therefore, in principle, the existence of closed timelike geodesics (CTGs) presents a bigger problem of breakdown of causality.The classical problem of the existence of closed geodesics in Riemannian geometry was solved by Hadamard [2] in two dimensions and by Cartan [3] in an arbitrary number of dimensions. As a topological problem, the existence of CTGs was proved by Tipler [4] in a class of four-dimensional compact Lorentz manifolds with covering space containing a compact Cauchy surface. In a compact pseudo-Riemaniann manifold with Lorentzian signature (Lorentzian manifold) Galloway [5] found sufficient conditions to have CTGs, see also [6].To the best of our knowledge there are four solution to the Einstein equations generated by matter with positive mass density that contain CTGs: a) Soares [7] found a class of cosmological models, solutions of EinsteinMaxwell equations, with a subclass where the timelike paths of matter are closed. For these models the existence of CTGs is demonstrated and explicit examples are given. These CTGs are not linearly stable [8]. b) Steadman [9] described the behavior of CTGs in a vacuum exterior for the van Stockum solution that represents an infinite rotating dust cylinder. For this solution explicit examples of CTCs and CTGs are shown. There are stable CTGs in this spacetime [8]. c) Bonnor and Steadman [10] studied the existence of CTGs in a spacetime with two spinning particles each one with magnetic moment equal

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Closed timelike geodesics in a gas of cosmic strings

Cited by 21 publications

References 19 publications

Potentially observable cylindrical wormholes without exotic matter in general relativity

Potentially observable cylindrical wormholes without exotic matter in general relativity

Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

Spinning Strings, Black Holes and Stable Closed Timelike Geodesics

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