Static Dark Fluid Thin Shells in Schwarzschild-de Sitter Spacetimes: Stability and Black Hole Shadows

TL;DR

This paper investigates the stability of static dark fluid thin shells in Schwarzschild-de Sitter spacetimes and explores how such shells can influence black hole shadows, providing insights into potential observational signatures.

Contribution

It introduces a novel analysis of static dark fluid thin shells, deriving stability conditions and demonstrating their effect on black hole shadow size in Schwarzschild-de Sitter backgrounds.

Findings

Stable shells exist only when mass ratio m_+/m_- > 1.

Positive-pressure shells are near the photon sphere, negative-pressure shells extend outward.

Shell properties can enlarge black hole shadows, affecting observational signatures.

Abstract

We study the existence and radial stability of static, spherically symmetric thin shells separating two Schwarzschild--de Sitter spacetimes with parameters $(m_\pm,\Lambda_\pm)$. Using the Israel junction formalism and a linear barotropic equation of state $p = \lambda(\sigma - \sigma_1)c^2$, we decouple the sound speed $c_s^2 = \lambda c^2$ from the equilibrium equation-of-state parameter $w_0 \equiv p_0 / (\sigma_0 c^2)$ and derive the effective potential governing radial dynamics. For observationally motivated parameters, stable configurations with $\sigma_0>0$ and $0<\lambda\leq1$ exist only when $m_+/m_- > 1$. Three distinct stability windows emerge, when $\lambda=1$: $-3/7 \lesssim w_0 \lesssim 1/2$ for $\Lambda_+ = \Lambda_-$, $-2/3 \lesssim w_0 \lesssim 1/2$ for $\Lambda_+ > \Lambda_-$ and $0 \lesssim w_0 \lesssim 1$ for $\Lambda_+ < \Lambda_-$. Positive-pressure shells ($w_0>0$) reside near the photon sphere, whereas negative-pressure shells ($w_0<0$) extend outward, reaching either the cosmological horizon or the static radius. Stability relies on the variation of $w(\sigma)$ with the surface energy density. Negative pressure (tension) stabilizes the system because the tension increases during expansion. Conversely, positive pressure stabilizes the system because the pressure increases during contraction. Finally, a static, stable, dark, fluid thin shell acts as a gravitational refractive layer that enlarges the black hole's shadow for a distant, static observer outside the shell. The effect depends on the shell radius $R_0$, the background parameters $(m_{\pm}, \Lambda_{\pm})$, and the equation-of-state. Dark fluid shells can be considered as theoretical toy models that illustrate qualitative effects. Future high-resolution black hole shadow observations could, in principle, use such models to explore how different equations of state might influence observable signatures.