Existence and Stability of Static Spherical Fluid Shells in a Schwarzschild-Rindler-anti-de Sitter Metric

Shells of matter sources with zero thickness play an important role in both electromagnetism and general relativity. They provide a useful laboratory for the exploration of new phenomena while at the same time they approximate smooth solutions such as domain walls . Thin shells are also useful in describing gravitational collapse or in constructing spherically symmetric vacuum solutions that avoid the presence of singularities. We demonstrate the existence of static, stable and thin spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime. This provides us with an alternative to the well-known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In constrast, when it comes to the SRAdS spacetime, the repulsion that leads to stability of the shell comes from a negative Rindler term while the Schwarzschild and anti-de Sitter terms are attractive. We demonstrate the existence of such stable spherical shells for three cases of fluid shells with the appropriate equations of state, i.e. vacuum shell, stiff matter shell, and dust shell. To do so, we also identify the metric parameter conditions that need to be satisfied in order to have shell stability in each case. The vacuum stable shell solution in the SRAdS spacetime is consistent with previous studies by two of the authors that demonstrated the existence of stable spherical scalar field domain walls in the SRAdS spacetime.