Splitting thin shells of counter rotating particles and their thick Einstein-Vlasov counterparts

REINALDO J. GLEISER; MARCOS A. RAMIREZ

México DF

Congreso; 19 International Conference on General Relativity and Gravitation; 2010

Instituto de Ciencias Nucleares - Universidad Nacional Autónoma de México

<!-- @page { size: 21cm 29.7cm; margin: 2cm } P { margin-bottom: 0.21cm } --> In this work we study the dynamics of self gravitating spherically symmetric thin shells made of counter rotating particles. We consider all possible velocity distributions for the particles, and show that the equations of motion by themselves do not constrain this distribution. We therefore consider the dynamical stability of the resulting configurations under several possible processes. This include the stability of static configurations as a whole, where we find a lower bound for the compactness of the shell. We analyse also the stability of the single particle orbits and find conditions for "single particle evaporation". In the case of a shell with particles whose angular momentum are restricted to two values, we consider the conditions for stability under splitting into two separate shells. This analysis leads to the conclusion that under certain conditions, that are given explicitly, an evolving shell may split into two or more separate shells. We provide explicit examples to illustrate this phenomenon. We also include a derivation of the thick to thin shell limit for an Einstein shell that shows that the limiting distribution of angular momenta is unique, covering continuously a finite range of values. Finally we deal with Einstein-Vlasov systems which are static, spherically symmetric and whose particles can only have a discrete set of values for their angular momentum. We prove some general properties which hold for a wide class of these shells and compare with previous results. We also develop a concrete family of shells and for these we provide arguments for the existence of a thin shell limit, showing that this limit, if exists, is in accordance with the thin shells that we have analysed before.