We study the existence and radial stability of static, spherically symmetric thin shells joining two Schwarzschild–de Sitter (SdS) spacetimes $(m_{\pm },{\mathrm{\Lambda }}_{\pm })$. Using the Israel junction formalism, we map the stable equilibria ($V_{\mathrm{eff}}^{\prime \prime }>0$) of the effective potential. Near the equilibrium radius $R_0$ the shell’s surface density $\sigma$ and pressure $p$ obey the linearized barotropic law $p=p_0+c_s^2(\sigma -{\sigma }_0)$, with sound speed $c_s^2=\lambda c^2$. Since $c_s^2$ is independent of the equilibrium ratio $w_0\equiv p_0/({\sigma }_0{c}^2)$, tension shells ($w_0<0$) stay radially stable with real $c_s$. Fixing ${\mathrm{\Lambda }}_{+}$ so that its vacuum energy density equals the critical density (Planck 2018), and taking $m_{-}$ representative of astrophysical black holes, we systematically map the stable equilibria $(R_0,{\sigma }_0)$ over $(m_{\pm },{\mathrm{\Lambda }}_{\pm },\lambda ,w_0)$ and find that stable shells with ${\sigma }_0>0$ and $0<\lambda \le 1$ exist only for $m_{+}/m_{-}>1$, at three scales—the photon sphere, the SdS static radius, and the cosmological horizon. At $\lambda =1$ the numerical windows, checked against the analytic test-shell bounds, are $(1-\sqrt{13})/6\lesssim w_0\lesssim 1/2$ (${\mathrm{\Lambda }}_{+}={\mathrm{\Lambda }}_{-}$), $-2/3\lesssim w_0\lesssim 1/2$ (${\mathrm{\Lambda }}_{+}>{\mathrm{\Lambda }}_{-}$), and $0\lesssim w_0$ (${\mathrm{\Lambda }}_{+}<{\mathrm{\Lambda }}_{-}$). Positive-pressure shells ($0\lesssim w_0\lesssim 1/2$) may sit near the photon sphere for any ordering of ${\mathrm{\Lambda }}_{+}/{\mathrm{\Lambda }}_{-}$. Additionally, when ${\mathrm{\Lambda }}_{+}<{\mathrm{\Lambda }}_{-}$ with $w_0\gtrsim 0$, they may also sit at the static-radius scale. Tension shells are absent for ${\mathrm{\Lambda }}_{+}<{\mathrm{\Lambda }}_{-}$; for ${\mathrm{\Lambda }}_{+}={\mathrm{\Lambda }}_{-}$, they reach the cosmological horizon scale; for ${\mathrm{\Lambda }}_{+}>{\mathrm{\Lambda }}_{-}$, they are confined to the static-radius scale. Finally, we compute the dark fluid shell’s imprint on the SdS black-hole shadow seen by a static observer at varying radial distance; the radially stable tension shells of interest sit near the static radius, where the deviation likely lies beyond observational reach.

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• Classical black holes
• General relativity
• Gravitation
• Astronomical black holes