Spatial Kasner Solution and an Infinite Slab with a Constant Energy Density |
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Authors: | Kamenshchik A Yu Vardanyan T |
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Institution: | 1.Dipartimento di Fisica e Astronomia, Università di Bologna and Istituto Nazionale di Fisica Nucleare, Bologna, 40126, Italy ;2.Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 117940, Russia ;3.Dipartimento di Fisica e Chimica, Università di L’Aquila, Coppito, L’Aquila, 67100, Italy ;4.Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso, Assergi, L’Aquila, 67010, Italy ; |
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Abstract: | We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and Weyl-Levi-Civita spacetimes outside the slab. We also show that there are solutions that can be matched with general anisotropic Kasner spacetime outside the slab. In any case, it is impossible to avoid the presence of the Kasner type singularities in contrast to the well-known case of spherical symmetry, where by matching the internal Schwarzschild solution with the external one, the singularity in the center of coordinates can be eliminated. |
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