Dark energy influenced compact spheres under Karmarkar condition

Abstract

This paper investigates the viability and stability of anisotropic dark energy stars using the embedding class-1 technique within Einstein’s general relativity. The widely used Krori–Barua ansatz is adopted for the temporal metric component, while the radial counterpart is derived by enforcing the Karmarkar condition. To close the system, we introduce an equation of state in which the dark energy density is directly proportional to the isotropic baryonic fluid density, with the proportionality parameter $\varpi$. The model’s unknown parameters are determined by applying junction conditions between the interior solution and the Schwarzschild exterior manifold. A comprehensive physical analysis ensures the regularity and consistency of metric potentials and state determinants. The compactness factor and gravitational redshift provide insights into stellar objects such as PSR J1903+327, SMC X-4, LMC X-4 and Her X-1. Furthermore, energy bounds validate the model’s physical plausibility, while stability is examined through the Tolman–Oppenheimer–Volkoff equation, causality condition, Zeldovich criterion and adiabatic index. The results indicate that, for the observed masses and radii of the selected stellar objects, the proposed embedded model remains physically consistent, offering a viable and stable description of anisotropic dark energy stars.