Electrically Charged Quark Stars in $4D$ Einstein-Gauss-Bonnet Gravity

Abstract: In this work we study the properties of compact spheres made of a charged perfect fluid with a MIT bag model EoS for quark matter. Considering static spherically symmetric spacetime we derive the hydrostatic equilibrium equations in the recently formulated four dimensional Einstein-Gauss-Bonnet ($4D$ EGB) gravity theory. In this setting, the modified TOV equations are solved numerically with the aim to investigate the impact of electric charge on the stellar structure. A nice feature of $4D$ EGB theory is that the Gauss-Bonnet term has a non-vanishing contribution to the gravitational dynamics in $4D$ spacetime. We therefore analyse the effects of Gauss-Bonnet coupling constant $\alpha$ and the charge fraction $\beta$ on the mass-radius ($M-R$) diagram and also the mass-central density $(M-\rho_c)$ relation of quark stars. Finally, we conclude that depending on the choice of coupling constant one could have larger mass and radius compared with GR and can also be relevant for more massive compact objects due to the effect of the repulsive Coulomb force.