Relativistic Charged Anisotropic Stars and Mass-Radius Analysis in Einstein-Euler-Heisenberg Gravity

We construct charged anisotropic compact-star models in general relativity coupled to Euler-Heisenberg (EH) nonlinear electrodynamics. The radial metric potential is of Finch-Skea type, the radial pressure obeys the linear relation [Formula: see text], and the electric field is obtained from the EH field equation for an enclosed charge [Formula: see text], solved consistently to first order in the EH coupling [Formula: see text]. The interior is matched to the exterior EH-corrected Reissner-Nordström geometry, and the model constants are fixed by the measured mass [Formula: see text] of PSR J1614−2230 together with a fiducial radius of [Formula: see text] km. All quantities are given in geometrized units with lengths in km; the coupling [Formula: see text], which has dimensions of length squared, is treated as an effective parameter restricted by the perturbative condition [Formula: see text]. The fiducial configuration has a central density of about [Formula: see text], compactness [Formula: see text] and surface redshift [Formula: see text]. The solution is regular, satisfies the energy conditions and causality, and respects both the Buchdahl bound and its charged generalization. Inside the perturbative window the EH terms change the stellar structure only at the level of [Formula: see text], so that the electromagnetic sector acts as a small correction to an anisotropic configuration whose stiffness is controlled by the equation of state. Keeping the equation of state fixed and varying the central density, we construct the mass-radius sequence. Physically admissible configurations reach about [Formula: see text], the Abreu condition holds up to about [Formula: see text]–[Formula: see text], and [Formula: see text] along the admissible branch. A larger charge parameter slightly raises the maximum admissible mass but narrows the range in which the Abreu condition is met.