Anisotropic solution for polytropic stars in 4D Einstein-Gauss-Bonnet gravity

Abstract: In the present work we have investigated a new anisotropic solution for polytropic star in the framework of $4D$ Einstein-Gauss-Bonnet (EGB) gravity. The possibility of determining the masses and radii of compact stars which puts some limitations on equation of state (EoS) above the nuclear saturation density. For this purpose, the $4D$ EGB field equations are solved by taking a generalized polytropic equation of state (EoS) with Finch-Skea ansatz. The generalized solution for anisotropic model has been tested for different values of Gauss-Bonnet constant $\alpha$ which satisfies all the physical criteria including causality with static stability via mass vs central mass density ($M-\rho_c$), Bondi and Abreu criterion. The adiabatic index shows a minor influence of the GB coupling constant whereas the central and surface redshifts in the EGB gravity always remain lower than the GR. We present the possibility of fitting the mass and radius for some known compact star via $M-R$ curve which satisfies the recent gravitational wave observations from GW 170817 event.