Self-gravitating splitting thin shells

MARCOS A. RAMIREZ

Brandenburg an der Havel

Workshop; Junior scientist Andrejewski days: 100 years of General Relativity; 2015

Universität Potsdam

We present a number of solutions of Einstein equations, in the sense of distributions, involving thin shells, and analyse their stability against separation of their constituents. This kind of solutions are important for a number of applications, like the analysis of the dynamics of globular clusters, cosmic bubbles in the early universe or brane-worlds. First, we deal with spherically symmetric shells made of Vlasov matter, and consider two different stability analysis against fragmentation: individual particle evaporation and separation of the particle ensemble into two sets. It is shown that dynamic shells may be composed by particles orbiting at different angular velocities, but in order to evolve stably as a single shell the angular momentum distribution cannot be arbitrary. In terms of the stability against separation of the particle ensemble, there are solutions that are initially stable, but turn unstable later in the evolution. In those cases a splitting solution can be constructed, where the original shell smoothly splits into a number of emergent shells. For a given initial data set, both the original shell without splitting and the splitting solution solve the Einstein equations coupled to matter, which illustrates a lack of uniqueness for the Cauchy problem. It is suggested that the unstable non-splitting solutions are not physical as they may not be thin-shell-limits of families of thick shell solutions. Finally, we extend the later stability analysis to shells composed of arbitrary non-interacting matter fields in isotropic spacetimes, with or without a cosmological constant. In particular, a SMS brane-world setting is considered, and it is shown that the same kind of instability typically appears for these models.