Construction of complexity-free anisotropic Dark Energy Stars

An enigmatic and forceful factor in the universe, dark energy is an essential component in driving the accelerated cosmic expansion. The interaction of such mysterious cosmic energy with gravitationally bound systems is, therefore, quite likely to occur, either directly or indirectly. In this context, we offer a concise method for investigating the possible interplay between ordinary matter and dark energy. We propose an astrophysical stellar model regulated by anti-gravitational energy that satisfies the zero-complexity constraint using the complexity factor formalism for static astrophysical stellar configurations, as originally suggested by Herrera (2018). The zero complexity condition helps to close the gravitational system in Einstein’s gravitational model. The temporal counterpart, $g_{tt}$, is established by applying the complexity-free constraint, whereas the radial metric component, $g_{rr}$, is obtained using the well-known Krori–Barua ansatz. Furthermore, we note that the dark energy parameter $\alpha$ affects the matter density and the stress components associated with normal matter of the complexity-free model. The resulting solutions are afterward examined in terms of geometrical and physical characteristics, such as stress components, density, energy conditions, and metric potentials. This is achieved by using the dense pulsar 4U 1538-52 as a representative model star. We have studied in detail how $\alpha$ affects our stellar model. The presented complexity-free model of dark energy is well-behaved and physically viable, as observed for different allowable values of $\alpha$.