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Conformally flat sources for the Linet–Tian spacetime

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Abstract

We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant \(\Lambda \), satisfying regularity conditions at the axis, to an exterior Linet–Tian spacetime. We prove that for \(\Lambda \le 0\) such matching is impossible. On the other hand, we show through simple examples that the matching is possible for \(\Lambda >0\). We suggest a physical argument that might explain these results.

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Notes

  1. We note that, in [29], a static cylinder of an incompressible fluid has been matched to the Levi-Civita solution.

  2. In the case \(\Lambda >0\), the hyperbolic functions in (22)–(24) are substituted by trigonometric ones.

  3. We note that in [19], the LT spacetime with \(\Lambda >0\) was matched to the toroidal Einstein static universe.

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Acknowledgments

We thank the referees for useful criticisms. IB and FM thank CMAT, Univ. Minho, for support through the FEDER Funds—“Programa Operacional Factores de Competitividade COMPETE” and FCT Project Est-C/MAT/UI0013/2011. FM is supported by FCT projects PTDC/MAT/108921/2008 and CERN/FP/116377/2010. MFAdaSilva acknowledges the financial support from FAPERJ (no. 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 (no. 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, Rio de Janeiro, 20550-900, Brazil

    M. F. A. da Silva

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

    N. O. Santos

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

    N. O. Santos

Authors
  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. Conformally flat sources for the Linet–Tian spacetime. Gen Relativ Gravit 45, 519–530 (2013). https://doi.org/10.1007/s10714-012-1485-6

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