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.