Energy–Momentum–Squared Gravity: Charged Quark Star Solutions with Unified Interacting Matter

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Abstract We investigate the equilibrium structure of electrically charged quark stars within the framework of energy-momentum-squared gravity (EMSG), adopting a unified interacting quark-matter equation of state that incorporates perturbative QCD corrections, color superconductivity, and finite-strange-quark-mass effects. By solving the modified Tolman-Oppenheimer-Volkoff equations over a broad range of EMSG coupling strengths and interaction parameters, we show that the inclusion of electric charge substantially increases both the maximum mass and radius compared with neutral configurations. For strong negative couplings and pronounced interaction strengths, the resulting stellar models reach masses close to $3\,M_{\odot}$ with compactness ratios of order $0.34$, consistent with the high-mass compact object inferred from GW190814. The presence of charge reduces the central density at maximum mass by approximately $10$--$15\%$ while maintaining full compliance with causality requirements. Furthermore, comparisons with observational constraints from PSR J1614$-$2230, J0348$+$0432, J0740$+$6620, J0952$-$0607, and recent NICER radius measurements indicate that charged EMSG configurations remain consistent with current astrophysical bounds over a wide parameter space. These results demonstrate that a moderate electric charge, when combined with nonlinear matter-geometry coupling, can support quark stars that are significantly more massive than those predicted in general relativity, underscoring the potential observational relevance of charged compact objects in modified gravity and multimessenger astrophysics.

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