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

  • Irene Brito
  • M. F. A. Da Silva
  • Filipe C. Mena
  • N. O. Santos
Research Article

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.

Keywords

General relativity Exact solutions Cylindrically symmetric spacetimes Geodesics Stability 

Notes

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Irene Brito
    • 1
  • M. F. A. Da Silva
    • 2
  • Filipe C. Mena
    • 1
    • 2
  • N. O. Santos
    • 3
    • 4
  1. 1.Centro de MatemáticaUniversidade do MinhoBragaPortugal
  2. 2.Departamento de Física Teórica, Instituto de FísicaUniversidade do Estado do Rio de JaneiroMaracanãBrazil
  3. 3.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  4. 4.Observatoire de Paris, LERMA(ERGA) CNRS–UMR 8112Université Pierre et Marie CurieIvry sur SeineFrance

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