Thick Einstein shells and their mechanical stability

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Abstract
Based on earlier work of Einstein (1939), the authors construct exact solutions of thick shells with zero radial pressure around black holes. The thick shells are built of layers of spherically symmetric thin shells containing collisionless particles travelling circular geodesics. Using the 'turning point' method of Poincare (1885) in the same way as Einstein they also demonstrate that thick shells which are big enough are mechanically stable. The inner radius of stable thick shells is smaller than the inner radius of stable thin shells. This result is relevant for thermal equilibrium black holes since these thick shells can have applications as heat baths producing the thermodynamic boundary conditions.