Theoretical Investigation of Dark Stars Admitting the Chaplygin Equation of State

Abstract

This study investigates the internal structure of compact stars models using the Chaplygin equation of state, a notable candidate for describing exotic matter due to its ability to manifest dark energy through an inverse pressure-density relationship. By integrating this equation of state into the framework of general relativity, we derive solutions that describe stable and physically realistic stellar configurations. The spacetime geometry within the stellar interior is governed by the Buchdahl metric potential, facilitating the construction of analytic models applicable to observed compact objects such as PSRJ1903 + 327, CenX - 3, and VelaX - 1, with respective masses of 1.667 M_⊙ , 1.49 M_⊙ , and 1.77 M_⊙ , and corresponding radii of 9.438 km, 9.178 km, and 9.56 km. To visualize the behavior of thermodynamic variables, two-dimensional contour plots are employed to illustrate the spatial variation of matter density and radial pressure, revealing centrally peaked distributions that decrease smoothly toward the boundary-consistent with expected stellar behavior. The model's validity is further examined using standard physical checks, including the satisfaction of energy conditions, causality constraints, and dynamical stability via the adiabatic index. The results support the Chaplygin gas as a compelling equation of state for describing compact astrophysical bodies and demonstrate the effectiveness of combining analytic methods with advanced graphical analysis in modeling relativistic stars.