Black holes and naked singularities from Anton-Schmidt's fluids

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.