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

TL;DR

This paper proves the existence and stability of static spherical fluid shells in a Schwarzschild-Rindler-anti-de Sitter spacetime, expanding understanding of stable configurations beyond gravastars with specific equations of state.

Contribution

It introduces stable spherical fluid shells in SRAdS spacetime with various equations of state, highlighting the role of a negative Rindler term in stability, differing from traditional gravastar models.

Findings

Stable shells exist for vacuum, stiff matter, and dust equations of state.

Conditions on metric parameters for shell stability are identified.

Vacuum shell solutions align with previous scalar field domain wall studies.

Abstract

We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(d\theta ^2 +\sin ^2 \theta d\phi ^2)$ with $f(r) = 1 -\frac{2Gm}{r} + 2 b r -\frac{\Lambda}{3}r^2$. This is 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 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 shell fluid equations of state: vacuum shell ($p=-\sigma$), stiff matter shell ($p=\sigma$) and dust shell ($p=0$) where $p$ is the shell pressure and $\sigma$ is the shell surface density. We also identify the metric parameter conditions that need to be satisfied for 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 sf stable spherical scalar field domain walls in the SRAdS spacetime.