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

TL;DR

This work develops a charged, anisotropic compact-star model within symmetric teleparallel gravity, specifically $f(Q)$–Euler–Heisenberg theory, employing the MIT Bag EoS to relate metric potentials and obtain an exact interior solution. The interior solution is smoothly matched to an exterior $f(Q)$–EEH spacetime using Darmois–Israel junction conditions, ensuring continuity of the metric and its derivatives and a surface vanishing radial pressure. Comprehensive physical viability checks—regularity, energy conditions, causality, adiabatic stability with $\Gamma>4/3$, and TOV equilibrium—are performed, revealing a stable, physically acceptable configuration for a range of the model parameter $\gamma$. The study finds that the $f(Q)$–EEH coupling stiffens the equation of state, enabling more massive and compact stars, with mass–radius relations consistent with observational data for several pulsars, thereby supporting the viability of this modified gravity framework for ultra-dense matter.

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 $Γ> \tfrac{4}{3}$ 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.

Figures (7)

• Figure 1: Graphical representation of interdependence of density $\rho$, pressures $p_r$, and $p_t$ along one an other with stellar radius $r$ for fixation of parameters (given in table-\ref{['tab1']}) and variation of parameters ($\gamma=-2.3$, $\gamma=-2.4$, $\gamma=-2.5$, $\gamma = -2.6$)
• Figure 2: Graphical representation of interdependence of anisotropy ($\Delta$) upon density $\rho$, pressures $p_r$, $p_t$, and radius $r$ for fixation of parameters (given in table-\ref{['tab1']}) and variation of parameters ($\gamma=-2.3$, $\gamma=-2.4$, $\gamma=-2.5$, $\gamma = -2.6$)
• Figure 3: Graphical representation of interdependence of Adiabatic index ($\Gamma$) upon density $\rho$, pressures $p_r$, and radius $r$ for fixation of parameters (given in table-\ref{['tab1']}) and variation of parameters ($\gamma=-2.3$, $\gamma=-2.4$, $\gamma=-2.5$, $\gamma = -2.6$)
• Figure 4: Graphical representation of interdependence of sound speeds $v_r^2$ and $v_t^2$ upon each othersand along radial coordinate $r$, and Tov forces upon density $\rho$, and radius $r$ for fixation of parameters (given in table-\ref{['tab1']}) and variation of parameters ($\gamma=-2.3$, $\gamma=-2.4$, $\gamma=-2.5$, $\gamma = -2.6$)
• Figure 5: Graphical representation of interdependence of equation of state parameters $w_r$ and $w_t$ upon each other, density $\rho$ and radial coordinate $r$ for fixation of parameters (given in table-\ref{['tab1']}) and variation of parameters ($\gamma=-2.3$, $\gamma=-2.4$, $\gamma=-2.5$, $\gamma = -2.6$)