Quark stars in regularized 4D Einstein-Gauss-Bonnet gravity: A perturbative QCD equation of state

Abstract

We investigate the equilibrium structure and stability of selfbound quark stars in the framework of regularized four-dimensional Einstein--Gauss--Bonnet (4DEGB) gravity, employing the perturbative QCD equation of state of Fraga, Kurkela and Vuorinen [1]. The equation of state, parameterised by a single renormalization-scale parameter $X$, contains no effective bag constant and defines the stellar surface entirely through the vanishing of the quark-matter pressure. We solve the modified Tolman-Oppenheimer--Volkoff equations derived from the scalar--tensor formulation of 4DEGB gravity for $X\in \{3,4\}$ and Gauss--Bonnet coupling $\alpha \in \{0,1,10\}{\mathrm{km}}^2$. For the soft EOS ($X=3$), the maximum mass increases from $2.0431M_{\odot }$ (GR) to $2.5013M_{\odot }$ at $\alpha =10{\mathrm{km}}^2$, with only the latter entering the PSR~J0952$-$0607 mass band. For the stiff EOS($X=4$), the GR baseline already yields $3.0415M_{\odot }$, and all configurations exceed both the GW190814 secondary mass and the PSR~J0952$-$0607 constraint. The compactness $C=M/R$ at maximum mass ranges from $0.2531$ to $0.3123$ across all configurations, remaining well below the Buchdahl bound throughout. Radial profiles of the squared speed of sound confirm that $c_s^2<1/3$ holds pointwise throughout the stellar interior for all parameter choices, establishing that the quark matter remains sub-conformal and causal inside the maximum-mass star. These results demonstrate that higher-curvature corrections in 4DEGB gravity systematically enhance the maximum supported mass of perturbative QCD quark stars, with the stiff ($X=4$) branch already exceeding the most massive compact objects currently observed even at the GR level, while the soft ($X=3$) branch requires $\alphaGB \sim 10\,\mathrm{km}^2$ to approach those thresholds.

14 pages, 7 figures