Relativistic dynamics of cylindrical shells of counter-rotating particles

HAMITY, V. H.; CÉCERE, M. A.; BARRACO DÍAZ, D. E.

GENERAL RELATIVITY AND GRAVITATION

SPRINGER/PLENUM PUBLISHERS

Año: 2009 vol. 41 p. 2657 - 2676

0001-7701

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 counterrotating 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.