Adopting the Tolman–Oppenheimer–Volkoff formalism, we propose a new analytical solution for a static and spherically symmetric black hole where the cosmological constant is generalized to a non-isotropic Anton–Schmidt fluid acting as a unified dark energy–dark matter source. Our novel result can describe a black hole in energetic equilibrium with the surrounding universe. We thus investigate the interplay between the mass of the black hole and the parameters of the Anton–Schmidt equation of state, and physically interpret the solution as a family of space–time metrics that may describe both Schwarzschild–de Sitter black holes and naked singularities. The result opens a new window for further constraining the physical properties of the cosmic fluid using the Event Horizon Telescope results, which complement the analysis relying on classical cosmological observations.

我们采用Tolman–Oppenheimer–Volkoff形式主义，为静态和球对称的黑洞提出了一种新的解析解决方案，其中宇宙常数被推广到非等向性的Anton-Schmidt流体，作为统一的暗能量-暗物质源。我们的新结果可以描述与周围宇宙处于能量平衡的黑洞。因此，我们研究了黑洞质量与Anton-Schmidt状态方程参数之间的相互作用，并从物理上将解决方案解释为一个时空度量族，可以描述Schwarzschild-de Sitter黑洞和裸奇点。结果打开了一个新窗口，可使用“事件地平线望远镜”结果进一步限制宇宙流体的物理特性，