Polytropic anti-de Sitter black hole

In the present study, we mainly discuss the features of polytropic anti-de Sitter (PAdS) black hole solution, which can be taken into account also as a stable configuration for dark energy stars. A dark energy star is a hypothetical compact astrophysical object and it has gained astrophysical relevance in literature for several reasons, for instance, it may be another interpretation for observations of astronomical black hole candidates. The idea basically points out that falling matter is transformed into dark energy (or vacuum energy), as the matter falls through the event horizon. In the first step of our investigation, assuming thermodynamical parameters of the asymptotically AdS black hole are identical to those introduced for the generalized polytropic gas, we obtain an exact solution for the metric function describing interior domain of the PAdS black hole. Then, we investigate the physical features of intermediate (shell) region. Subsequently, we describe physical properties like energy conditions and hydrostatic equilibrium via mathematical calculations as well as graphical analyses. In the final step, because black holes can be naturally regarded as a thermal device, we focus on a heat engine process for the PAdS black hole and obtain an analytical expression for the efficiency in terms of entropy and temperature.