We show that Einstein’s field equations with a negative cosmological constant
    can admit black hole solutions whose thermodynamics coincides with that of
    logotropic fluids, recently investigated to heal some cosmological and
    astrophysical issues. For this purpose, we adopt the Anton-Schmidt equation of
    state, which represents a generalized version of logotropic fluids. We thus
    propose a general treatment to obtain an asymptotic anti-de Sitter metric,
    reproducing the thermodynamic properties of both Anton-Schmidt and logotropic
    fluids. Hence, we explore how to construct suitable spacetime functions,
    invoking an event horizon and fulfilling the null, weak, strong and dominant
    energy conditions. We further relax the strong energy condition to search for
    possible additional solutions. Finally, we discuss the optical properties
    related to a specific class of metrics and show how to construct an effective
    refractive index depending on the spacetime functions and the thermodynamic
    quantities of the fluid under study. We also explore possible departures with
    respect to the case without the fluid.

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