Effect of radiative gravitational modes on the dynamics of a cylindrical shell of counterrotating particles.

REINALDO J. GLEISER Y MARCOS A. RAMIREZ

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Año: 2012 vol. 85 p. 1 - 12

0556-2821

In this paper we consider some aspects of the relativistic dynamics of a cylindrical shell of counterrotatingparticles. In some sense these are the simplest systems with a physically acceptable matter contentthat display in a well-defined sense an interaction with the radiative modes of the gravitational field. Thesesystems have been analyzed previously, but in most cases resorting to approximations, or considering aparticular form for the initial value data. Here we show that there exists a family of solutions where thespace time inside the shell is flat and the equation of motion of the shell decouples completely from thegravitational modes. The motion of the shell is governed by an equation of the same form as that of aparticle in a time-independent one-dimensional potential. We find that under appropriate initial conditionsone can have collapsing, bounded periodic, and unbounded motions. We analyze and solve also thelinearized equations that describe the dynamics of the system near a stable static solutions, keeping aregular interior. The surprising result here is that the motion of the shell is completely determined by theconfiguration of the radiative modes of the gravitational field. In particular, there are oscillating solutionsfor any chosen period, in contrast with the ‘‘approximately Newtonian plus small radiative corrections’’motion expectation. We comment on the physical meaning of these results and provide some explicitexamples. We also discuss the relation of our results to the initial value problem for the linearizeddynamics of the shell.