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Are there any models with homogeneous energy density?

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Abstract

By applying a recent method—based on a tetrad formalism in General Relativity and the orthogonal splitting of the Riemann tensor—to the simple spherical static case, we found that the only static solution with homogeneous energy density is the Schwarzschild solution and that there are no spherically symmetric dynamic solutions consistent with the homogeneous energy density assumption. Finally, a circular equivalence is shown among the most frequent conditions considered in the spherical symmetric case: homogeneous density, isotropy in pressures, conformally flatness and shear-free conditions. We demonstrate that, due to the regularity conditions at the center of the matter distribution, the imposition of two conditions necessarily leads to the static case.

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Acknowledgements

J.O. and J.L.H.-P. acknowledge financial support from Fondo Europeo de Desarrollo Regional (FEDER) (Grant FIS2015-65140-P) (MINECO/FEDER). J.O acknowledges hospitality of School of Physics of the Industrial University of Santander, Bucaramanga Colombia. L.A.N. gratefully acknowledge the financial support of the Vicerrectoría de Investigación y Extensión de la Universidad Industrial de Santander and the financial support provided by COLCIENCIAS under Grant No. 8863

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Authors and Affiliations

  1. Departamento de Matemática Aplicada and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Salamanca, Spain

    J. Ospino & J. L. Hernández-Pastora

  2. Escuela de Física, Universidad Industrial de Santander, Bucaramanga, Colombia

    H. Hernández & L. A. Núñez

  3. Departamento de Física, Universidad de Los Andes, Mérida, Venezuela

    H. Hernández & L. A. Núñez

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  1. J. Ospino
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  2. J. L. Hernández-Pastora
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  3. H. Hernández
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  4. L. A. Núñez
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Correspondence to J. Ospino.

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Ospino, J., Hernández-Pastora, J.L., Hernández, H. et al. Are there any models with homogeneous energy density?. Gen Relativ Gravit 50, 146 (2018). https://doi.org/10.1007/s10714-018-2467-0

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