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We consider the dynamics of timelike spherical thin matter shells in vacuum.A general formalism for thin shells matching two arbitrary spherical spacetimesis derived, and subsequently specialized to the vacuum case. We first examinethe relative motion of two dust shells by focusing on the dynamics of theexterior shell, whereby the problem is reduced to that of a single shell withdifferent active Schwarzschild masses on each side. We then examine thedynamics of shells with non-vanishing tangential pressure $p$, and show thatthere are no stable--stationary, or otherwise--solutions for configurationswith a strictly linear barotropic equation of state, $p=\alpha\sigma$, where$\sigma$ is the proper surface energy density and $\alpha\in(-1,1)$. For {\emarbitrary} equations of state, we show that, provided the weak energy conditionholds, the strong energy condition is necessary and sufficient for stability.We examine in detail the formation of trapped surfaces, and show explicitlythat a thin boundary layer causes the apparent horizon to evolvediscontinuously. Finally, we derive an analytical (necessary and sufficient)condition for neighboring shells to cross, and compare the discrete shell modelwith the well-known continuous Lema\^{\i}tre-Tolman-Bondi dust case.Comment: 25 pages, revtex4, 4 eps figs; published in Phys. Rev.

Relativistic shells: Dynamics, horizons, and shell crossing