Stability of the Schwarzschild-de Sitter model

From a study of the shape of a spacelike, three-cylindrical transition layer separating a de Sitter future region from a Schwarzschild past region, we show that the uniform configuration (in the sense that the layer's radius is not a function of the layer's proper distance along its axis) considered by Frolov, Markov, and Mukhanov [Phys. Lett. B 216, 272 (1989)] is a stable configuration (in the sense that, when perturbed, the three-cylinder does not tend to shrink down to a point as a cone). We also show that this model does not require fine-tuning since a variation of the layer's internal parameters from the uniform configuration does not destroy the three-cylinder but induces spatial oscillations in its radius.