Stellar structure in a Newtonian theory with variable $G$
J\'ulio C. Fabris, T\'ulio Ottoni, J\'unior D. Toniato and, Hermano Velten
TL;DR
This paper investigates how a Newtonian theory with a spatially varying gravitational constant $G$, inspired by Brans-Dicke theory, affects stellar structure, providing a modified Lane-Emden equation and analyzing the impact of the theory parameter.
Contribution
It introduces a modified Lane-Emden equation for stars in a Newtonian theory with variable $G$, exploring the influence of the Brans-Dicke-like parameter on stellar properties.
Findings
The modified Lane-Emden equation is derived for variable $G$ scenarios.
The parameter $\omega$ significantly affects stellar equilibrium configurations.
Solutions vary with different polytropic indices, illustrating the theory's impact.
Abstract
A Newtonian-like theory inspired by the Brans-Dicke gravitational Lagrangian has been recently proposed. 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 varying 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 , the analogue of the Brans-Dicke parameter, on the physical properties of stars is discussed.
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