Stellar Structure in a Newtonian Theory with Variable G

A Newtonian-like theory inspired by the Brans-Dicke gravitational Lagrangian has been recently proposed by us. For static configurations, the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work, we focus on the stellar hydrostatic equilibrium structure in such a varying Newtonian gravitational coupling G scenario. A modified Lane-Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter omega, the analogue of the Brans-Dicke parameter, in the physical properties of stars is discussed.