1207.6810 (Marcos A. Ramirez)
Marcos A. Ramirez
We consider a singular timelike spherical hypersurface embedded in a D-dimensional spherically symmetric bulk space-time. We analyze the different possibilities regarding the orientation of the gradient of the standard $r$ coordinate in relation to the shell. The matter content of the shell is described by a number of non-interacting spherically symmetric matter fields. We analyze the dynamics according to Einstein's equations for matter satisfying certain energy conditions. Then we show that, under some circumstances, the system at a given proper time becomes unstable against an infinitesimal separation of non-interacting constituents. In particular, we consider the case where the shell is filled with collisionless particles that move in trajectories of constant angular momentum, and show that, for shells whose angular momentum distribution is discrete, the instability that we described before takes place. We also find this instability when the components are fluids with certain equations of state. We give explicit examples and construct solutions that represent a shell that splits into two shells. Then we extend those results for 5-dimensional Schwarzschild-AdS bulk space-times, which is a typical scenario for brane-world models, and show that the same kind of splitting solution can be constructed. Finally we discuss possible interpretations of these features and their relation to the initial value problem with concentrated sources.
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http://arxiv.org/abs/1207.6810
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