Structure and Mass-Radius Stability of Charged Compact Objects in Symmetric Teleparallel Euler-Heisenberg Gravity

TL;DR

This paper develops a new relativistic model for charged anisotropic compact stars within $f(Q)$-Euler-Heisenberg gravity, demonstrating physical viability, stability, and consistent mass-radius relations through exact solutions and graphical analysis.

Contribution

It introduces an exact solution for charged anisotropic stars in $f(Q)$-Euler-Heisenberg gravity using the MIT bag model, linking modified gravity with stellar structure analysis.

Findings

Model satisfies regularity, energy, and causality conditions.

Star remains in equilibrium with balanced forces.

Mass-radius and redshift profiles are physically consistent.

Abstract

In this work, we develop a new relativistic model for a charged anisotropic compact star in the framework of modified symmetric teleparallel gravity, namely $f(Q)$-Euler-Heisenberg gravity. By employing the MIT bag model equation of state, we establish a relation between the metric potentials, leading to an exact solution of the field equations for an anisotropic fluid configuration coupled with a non-linear electromagnetic source. The interior spacetime is smoothly matched with the exterior geometry calculated from the theoretical setup of $f(Q)$-Euler-Heisenberg gravity using the Darmois-Israel junction conditions, ensuring the continuity of the metric functions and their derivatives at the stellar boundary. The physical viability of the model is examined through regularity, energy, and causality conditions, all of which are satisfied throughout the stellar interior. The study highlights how the pressure anisotropy, the propagation speeds of sound, and the Tolman-Oppenheimer-Volkoff balance condition are interconnected, showing that the star remains in mechanical equilibrium only when the gravitational, hydrostatic, electric, and anisotropic contributions counterbalance one another appropriately. The dynamical stability of the configuration is further supported by the requirement $\Gamma > \tfrac{4}{3}$ for the adiabatic index, indicating resilience against small radial perturbations. The plots of compactness, surface redshift, and the mass--radius profiles confirm that all physical quantities behave regularly and vary smoothly throughout the stellar interior. We graphically plotted the mass-radius curves.