Abstract We address the equilibrium configurations and stability properties of anisotropic compact stars whose interior is described by a modified Chaplygin gas (MCG) equation of state in the framework of the regularized four-dimensional Einstein–Gauss–Bonnet (4DEGB) theory. Applying a quasi-local prescription for the pressure anisotropy, we derive the modified Tolman–Oppenheimer–Volkoff (TOV) equations and integrate them numerically over a large parameter space in the Gauss–Bonnet coupling α and the degree of anisotropy β. We provide mass–radius sequences, mass-compactness, energy density, and pressure profiles, and perform a full stability analysis based on the turning-point criterion, the radial adiabatic index ᵣ γ r, and the radial and transverse sound speeds vᵣ² v r 2 and vₜ² v t 2. Our results show that positive α and positive anisotropy (> 0) (β > 0) systematically increase the maximum mass and radius, enabling then configurations that exceed 2\, M_ 2 M ⊙ while still obeying causality and the modified Buchdahl bound in 4DEGB gravity. A comparison with the latest astrophysical constraints (NICER, GW170817, GW190814, and massive-pulsar measurements) identifies regions of the (, ) (α, β) parameter space that are observationally allowable. In conclusion, anisotropic dark-energy stars in 4DEGB gravity provide viable, observationally testable ultra-compact alternatives to normal neutron stars and black holes, and also potentially open rich avenues for further multi-messenger searches for higher-curvature effects.
Pradhan et al. (Thu,) studied this question.