Abstract
This paper provides the analysis of relativistic compact star models in the context of general relativity with the addition of the dark matter (DM) effect in the form of the Burkert profile. Since DM could potentially influence the dynamics of galaxies, as well as the internal structure of compact astrophysical objects, we consider four famous neutron stars (PSR J0740+6620, PSR J0348+0432, PSR J1614-2230, and 4U 1724-207) using their observed masses together with representative radii as a physical constraint and discuss the effect of DM on the characteristic features of these star models. This adopted density profile acts as an effective matter density distribution for the construction of regular compact star configurations and is not meant to be treated as a realistic two-fluid DM admixed system. We set one metric potential and find the other based on a highly motivated DM density profile, in a spherically symmetric, static spacetime. This provides a consistent solution to the Einstein field equations. These configurations are scrutinized through essential physical metrics, the effective equation of state, energy conditions, conservation equation, adiabatic index, active gravitational mass, compactness, and redshift to evaluate physical viability and feasibility. The results are compatible with observational constraints and suitable parametric choices and show that DM clearly modifies the interior structure of compact stars, especially in the pressure evolution and gravitational characteristics. In summary, this work explores the influence of a Burkert-inspired cored matter distribution on the geometric and physical properties of compact stellar configurations.