Dark energy stars with cosmological constant as a black-hole mimickers

In this study, we investigated an interior solution of a static spherically symmetric dark energy star model incorporating anisotropic fluid and a state parameter of the type cosmological constant, achieved through parametrization of the Finch and Skea metric function. The motivation for this study stems from the lack of investigation of dark energy star models in relation to BHs in the previous studies, and from recent proposals suggesting that dark energy might originate inside BHs. This opens up the opportunity to explore the dark energy star model and establish its relationship with BHs. The structural profiles of the models, including mass function, energy density, compactness, surface redshift, and local acceleration due to gravity, were investigated. Analysis involving the matching of the exterior Schwarzschild vacuum solution to the interior spacetime at a junction interface was also explored. The results demonstrate that this solution is free of singularities, possessing outward gravitational repulsion with an infinite property near the surface boundary. Notably, the model exhibited an infinite redshift surface, and a compactness of one half, thus evading the Buchdahl limit. It fulfills the energy conditions except for the strong energy conditions and remains in a state of static equilibrium, upheld by both hydro-static and anisotropic forces. Numerical values of physical properties for various types of astrophysical BH candidates have been determined. Overall, the obtained model is physically unique and represents the most compact and extreme model of dark energy stars. Some features of this model resemble those of BHs, rendering it indistinguishable from BHs.