Thermodynamic analysis of black holes solution in non-conservative theory of gravity

We derive fresh exact solutions for the gravitational field equations within the framework of Rastall gravity, yielding various categories of black holes enveloped by fluids. This exploration incorporates specific values of the equation of state parameter, [Formula: see text]. To attain these solutions under Rastall gravity, we deliberate on feasible, distinctive selections of the Rastall parameter. By considering an anisotropic energy–momentum tensor, we formulate the field equations with the necessary symmetries for this solution type. Subsequently, we scrutinize energy conditions both generally and for particular [Formula: see text] values of the equation of state parameter. Furthermore, our analysis incorporates thermodynamic quantities, such as Hawking temperature and mass associated with the horizons of the solutions.