Charged polytropic compact stars in 4D Einstein-Gauss-Bonnet gravity

We have investigated the possibility of existing a class of compact charged spheres made of a charged perfect fluid in the context of recently proposed 4D Einstein-Gauss-Bonnet (EGB) gravity theory. The main mechanism is to rescale the Gauss-Bonnet (GB) coupling constant alpha -> alpha / (D - 4) in D dimensions and redefining the 4D gravity in the limit D -> 4. In this way, the GB term yields a non-trivial contribution to the gravitational dynamics in 4D. Our analysis is based on the assumption of a polytropic equation of state (E0S) and the charge density is taken to be proportional to the energy density. More specifically, we have derived the hydrostatic equilibrium equations in 4D EGB, and we have solved them numerically to obtain mass-radius relations for charged compact stars. Eventually we have found the mass-radius relation depending on the values of the GB coupling constant alpha and the charge fraction rho(ch)(r). In addition, we have studied the mass vs central mass density (M-epsilon(c)) relation, which identifies the boundary separating the stable configuration region from the unstable one. We have also obtained a relation between the electric charge inside the stellar region and the maximum mass of compact star in this gravity theory. Finally, we conclude that in such a scenario charged stars may exist in Nature, and that such a deviation may be observable in future astrophysical probes.