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Geodesics dynamics in the Linet–Tian spacetime with \(\Lambda <0\)

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Abstract

We investigate the geodesics’ kinematics and dynamics in the Linet–Tian metric with \(\Lambda <0\) and compare with the results for the Levi–Civita metric, when \(\Lambda =0\). This is used to derive new stability results about the geodesics’ dynamics in static vacuum cylindrically symmetric spacetimes with respect to the introduction of \(\Lambda <0\). In particular, we find that increasing \(|\Lambda |\) always increases the minimum and maximum radial distances to the axis of any spatially confined planar null geodesic. Furthermore, we show that, in some cases, the inclusion of any \(\Lambda <0\) breaks the geodesics’ orbit confinement of the \(\Lambda =0\) metric, for both planar and non-planar null geodesics, which are therefore unstable. Using the full system of geodesics’ equations, we provide numerical examples which illustrate our results.

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Acknowledgments

IB and FM thank CMAT, Univ. Minho, for support through the FEDER Funds-COMPETE and FCT Project Est-C/MAT/UI0013/2011. FM is also supported by FCT projects PTDC/MAT/108921/2008 and CERN/FP/123609/2011 and thanks the warm hospitality from Instituto de Física, UERJ, Rio de Janeiro, where this work was completed. MFAdaSilva acknowledges the financial support from FAPERJ (Nos. E-26/171.754/2000, E-26/171.533.2002, E-26/170.951/2006, E-26/110.432/2009 and E-26/111.714/2010), Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq—Brazil (Nos. 450572/2009-9, 301973/2009-1 and 477268/2010-2) and Financiadora de Estudos e Projetos—FINEP—Brazil.

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Authors and Affiliations

  1. Centro de Matemática, Universidade do Minho, 4710-057 , Braga, Portugal

    Irene Brito & Filipe C. Mena

  2. Departamento de Física Teórica, Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, 20550-900, Rio de Janeiro, Brazil

    M. F. A. Da Silva & Filipe C. Mena

  3. School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK

    N. O. Santos

  4. Observatoire de Paris, LERMA(ERGA) CNRS–UMR 8112, Université Pierre et Marie Curie, 94200 , Ivry sur Seine, France

    N. O. Santos

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  1. Irene Brito
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  2. M. F. A. Da Silva
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  3. Filipe C. Mena
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  4. N. O. Santos
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Correspondence to Filipe C. Mena.

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Brito, I., Da Silva, M.F.A., Mena, F.C. et al. Geodesics dynamics in the Linet–Tian spacetime with \(\Lambda <0\) . Gen Relativ Gravit 46, 1681 (2014). https://doi.org/10.1007/s10714-014-1681-7

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