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Collapsing spheres satisfying an “Euclidean condition”

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Abstract

We study the general properties of fluid spheres satisfying the heuristic assumption that theirs areal and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaître–Tolman–Bondi solution is obtained. In the dissipative case solutions are non-geodesic and are characterized by the fact that all non-gravitational forces acting on any fluid element produces a radial three-acceleration independent on its inertial mass.

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Authors and Affiliations

  1. Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, Venezuela

    L. Herrera

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

    N. O. Santos

  3. Laboratório Nacional de Computação Científica, Petrópolis, RJ, 25651-070, Brazil

    N. O. Santos

  4. Université Pierre et Marie Curie, LERMA(ERGA) CNRS, UMR 8112, 94200, Ivry, France

    N. O. Santos

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  1. L. Herrera
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  2. N. O. Santos
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Correspondence to L. Herrera.

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Herrera, L., Santos, N.O. Collapsing spheres satisfying an “Euclidean condition”. Gen Relativ Gravit 42, 2383–2391 (2010). https://doi.org/10.1007/s10714-010-0986-4

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  • DOI: https://doi.org/10.1007/s10714-010-0986-4

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