THICK EINSTEIN SHELLS AND THEIR MECHANICAL STABILITY

Based on earlier work of Einstein, we 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 in the same way as Einstein we 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 our thick shells can have applications as heat baths producing the thermodynamic boundary conditions.