Relativistic dynamics of cylindrical shells of counter-rotating particles |
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Authors: | Victor Hugo Hamity M A Cécere and D E Barraco |
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Institution: | 1.Fa.M.A.F.,Universidad Nacional de Córdoba, Ciudad Universitaria,Córdoba,Argentina |
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Abstract: | Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative
features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits of very
small radius. We study an analytical model of a relativistic cylindrical shell of counter-rotating particles using kinetic
theory for the matter and the junction conditions through the shell to obtain its equation of motion. The nature of the static
solutions are analyzed, both for a single shell as well as for two coaxial shells. In the latter case, we integrate numerically
the time dependent equation of motion of the external shell, when we neglect the wave components of the gravitational field
at the shells locations. We obtain solutions that correspond to shells that perform damped oscillations, collapse, or are
locally expanding. The collapse ends (numerically) when the external shell hits the interior shell. The numerically work also
shows that the radiation becomes important after the bounce of the external shell. |
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