This work is devoted to the recently introduced Einstein–Gauss–Bonnet gravity in four dimensions. This theory can bypass Lovelock’s theorem and avoids Ostrogradsky instability. The integrated part of this theory is the GB term which gives rise to a non-trivial contribution to the gravitational dynamics in the limit $D\to 4$. Our main interest is to explore a class of static, spherically symmetric compact objects made of strange matter. It is believed that at ultra-high densities, quark matter may exist in a variety of superconducting states, namely, the Color–Flavor-Locked (CFL) phase. With these equations of state (EoS) we explore the conditions under which compact stars are stable under extreme conditions in the context of $4D$ EGB gravity. In addition, the mass–radius relation is examined and the effects of the coupling constant ‘$\alpha$’ on the stellar model, energy conditions, speed of sound and adiabatic stability are studied. With the aim to find observational constraints on the GB constant of $4D$ EGB gravity, the mass–radius curve is determined satisfying the maximum mass constraint of $M\sim 2M_{\odot }$ for neutron stars. This feature may be relevant in view of recent observations claiming the existence of stable compact quark stars (hybrid neutron stars or strange stars).

这项工作专门针对最近引入的四个维度的爱因斯坦-高斯-引擎盖引力。该理论可以绕过洛夫洛克定理并避免Ostrogradsky不稳定性。该理论的组成部分是GB术语，它对极限内的引力动力学产生了不小的贡献$d\to 4$。我们的主要兴趣是探索一类由奇异物质制成的静态球对称紧凑物体。人们认为，在超高密度下，夸克物质可能以各种超导状态存在，即色偏锁相（CFL）。利用这些状态方程（EoS），我们探索了在极端条件下紧密恒星在极端条件下稳定的条件$4d$EGB重力。另外，检查了质量半径关系，以及耦合常数的影响。$\alpha$在恒星模型上，研究了能量条件，声速和绝热稳定性。为了找到对GB常数的观测约束$4d$ EGB重力，确定满足最大质量约束的质量半径曲线 $\mathrm{中号}〜2{\mathrm{中号}}_{\odot }$用于中子星。鉴于最近的观察声称存在稳定的紧凑夸克星（混合中子星或奇异星），因此该功能可能是相关的。