Stability of generic thin shells in conformally flat spacetimes

Abstract

Some important spacetimes are conformally flat; examples are the Robertson-Walker cosmological metric, the Einstein-de Sitter spacetime, and the Levi-Civita-Bertotti-Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., p = omega sigma. It is shown that, for the physical domain of., i.e., 0 < omega <= 1, such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated.