Relativistic stars in 4D Einstein-Gauss-Bonnet gravity

Abstract: In the present paper we investigate the structure of relativistic stars in 4D Einstein-Gauss-Bonnet gravity. The mass-radius relations are obtained for realistic hadronic and for strange quark star equations of state, and for a wide range of the Gauss-Bonnet coupling parameter $\alpha$. Even though the deviations from general relativity for nonzero values of $\alpha$ can be large enough, they are still comparable with the variations due to different modern realistic equations of state if we restrict ourselves to moderate value of $\alpha$. That is why the current observations of the neutron star masses and radii alone can not impose stringent constraints on the value of the parameter $\alpha$. Nevertheless some rough constraints on $\alpha$ can be put. The existence of stable stellar mass black holes imposes $\sqrt{\alpha}\lesssim 2.6 {\rm km}$ for $\alpha>0$ while the requirement that the maximum neutron star mass should be greater than two solar masses gives $\sqrt{|\alpha|}\lesssim 3.9 {\rm km}$ for $\alpha<0$. We also present an exact solution describing the structure of relativistic stars with uniform energy density in 4D Einstein-Gauss-Bonnet gravity.