Charged quark stars and extreme compact objects in regularized 4D Einstein-Gauss-Bonnet gravity

Since the derivation of a well-defined $D\ensuremath{\rightarrow}4$ limit for four-dimensional Einstein Gauss-Bonnet (4DEGB) gravity coupled to a scalar field, there has been interest in testing it as an alternative to Einstein's general theory of relativity. Using the Tolman-Oppenheimer-Volkoff equations modified for charge and 4DEGB gravity, we model the stellar structure of charged, noninteracting quark stars. We find that increasing the Gauss-Bonnet coupling constant $\ensuremath{\alpha}$ or the charge $Q$ both tend to increase the mass-radius profiles of quark stars described by this theory, allowing a given central pressure to support larger quark stars in general. We also derive a generalization of the Buchdahl bound for charged stars in 4DEGB gravity. As in the uncharged case, we find that quark stars can exist below the general relativistic Buchdahl bound and Schwarzschild radius $R=2M$, due to the lack of a mass gap between black holes and compact stars in the 4DEGB theory. Even for $\ensuremath{\alpha}$ well within current observational constraints, we find that quark star solutions in this theory can describe extreme compact charged objects, objects whose radii are smaller than what is allowed by general relativity.