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Schwarzschild-de Sitter时空中的静态暗流体薄壳：稳定性与黑洞阴影

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

Department of Physics, University of Ioannina（伊奥阿尼纳大学物理系）

Dimitrios Efstratiou, Evangelos Achilleas Paraskevas, Leandros Perivolaropoulos

备注：
This version contains 16 pages and 5 figures. The manuscript matches the version accepted for publication in Physical Review D. The numerical analysis file used for the construction of the figures may be found at https://github.com/Dimitrios1993/Static-Thin-Shells-in-SdS-Spacetimes
发表信息：
Phys. Rev. D 114, 064089 (2026)
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AI总结：

利用Israel结理论，研究连接两个SdS时空的静态球对称薄壳的存在性与径向稳定性，发现稳定壳存在于特定质量比和尺度，并计算暗流体壳对黑洞阴影的影响。

摘要：

我们研究了连接两个Schwarzschild-de Sitter (SdS)时空$(m_\pm,\Lambda_\pm)$的静态、球对称薄壳的存在性和径向稳定性。利用Israel结形式，我们映射了有效势的稳定平衡点($V_{\mathrm{eff}}''>0$)。在平衡半径$R_0$附近，壳的表面密度$\sigma$和压力$p$服从线性化的正压定律$p=p_0+c_s^2(\sigma-\sigma_0)$，其中声速$c_s^2=\lambda c^2$。由于$c_s^2$与平衡比值$w_0\equiv p_0/(\sigma_0 c^2)$无关，张力壳($w_0<0$)在实$c_s$下保持径向稳定。固定$\Lambda_+$使其真空能量密度等于临界密度(Planck 2018)，并取$m_-$代表天体物理黑洞，我们系统地映射了$(R_0,\sigma_0)$在$(m_\pm,\Lambda_\pm,\lambda,w_0)$上的稳定平衡点，发现具有$\sigma_0>0$和$0<\lambda\le1$的稳定壳仅存在于$m_+/m_->1$，且位于三个尺度——光子球、SdS静态半径和宇宙视界。在$\lambda=1$时，数值窗口（与解析测试壳边界对比）为$(1-\sqrt{13})/6\lesssim w_0\lesssim 1/2$ ($\Lambda_+=\Lambda_-$), $-2/3\lesssim w_0\lesssim 1/2$ ($\Lambda_+>\Lambda_-$), 和$0\lesssim w_0$ ($\Lambda_+<\Lambda_-$)。正压壳($0\lesssim w_0\lesssim 1/2$)位于光子球附近，而$w_0\gtrsim1/2$的壳位于静态半径尺度附近；张力壳在$\Lambda_+=\Lambda_-$时达到宇宙视界尺度，在$\Lambda_+>\Lambda_-$时仅达到静态半径尺度，在$\Lambda_+<\Lambda_-$时不存在。最后，我们计算了暗流体壳对由不同径向距离的静态观测者看到的SdS黑洞阴影的影响。

英文摘要：

We study the existence and radial stability of static, spherically symmetric thin shells joining two Schwarzschild-de Sitter (SdS) spacetimes $(m_\pm,Λ_\pm)$. Near the equilibrium radius $R_0$ the shell's surface density $σ$ and pressure $p$ obey the linearized barotropic law $p=p_0+c_s^2(σ-σ_0)$, with sound speed $c_s^2=λc^2$. Since $c_s^2$ is independent of the equilibrium ratio $w_0\equiv p_0/(σ_0 c^2)$, tension shells ($w_0<0$) stay radially stable with real $c_s$. Fixing $Λ_+$ 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 $(R_0,σ_0)$ over $(m_\pm,Λ_\pm,λ,w_0)$ and find that stable shells with $σ_0>0$ and $0<λ\leq 1$ exist only for $m_+/m_->1$, at three scales---the photon sphere, the SdS static radius, and the cosmological horizon. At $λ=1$ the numerical windows, checked against the analytic test-shell bounds, are $(1-\sqrt{13})/6\lesssim w_0\lesssim 1/2$ ($Λ_+=Λ_-$), $-2/3\lesssim w_0\lesssim 1/2$ ($Λ_+>Λ_-$), and $0\lesssim w_0$ ($Λ_+<Λ_-$). Positive-pressure shells ($0\lesssim w_0\lesssim 1/2$) may sit near the photon sphere for any ordering of $Λ_+/Λ_-$. Additionally, when $Λ_+<Λ_-$ with $w_0\gtrsim0$, they may also sit at the static-radius scale. Tension shells are absent for $Λ_+<Λ_-$; for $Λ_+=Λ_-$, they reach the cosmological horizon scale; for $Λ_+>Λ_-$, 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.

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