Abstract
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 ω, the analogue of the Brans–Dicke parameter, in the physical properties of stars is discussed.
Highlights
Are the fundamental constants of physics truly constants? This is a long-standing question, perhaps dating back to the identification of these constants themselves
We can identify, in particular, four fundamental constants, each one connected with a given theoretical structure: the Planck constant, h, which defines the quantum world; c, the speed of light, which is the limit velocity and is related to the relativistic domain; the Newtonian gravitational constant, G, which indicates the presence of the gravitational interaction; k B, the Boltzmann constant related to thermodynamics
The gravitational coupling G was the first one to be identified, it is the one that is known with the poorest precision: its value is determined up to the 10−4 order [1]
Summary
Are the fundamental constants of physics truly constants? This is a long-standing question, perhaps dating back to the identification of these constants themselves. The gravitational coupling G was the first one to be identified, it is the one that is known with the poorest precision: its value is determined up to the 10−4 order [1] This is a consequence of the universality of this fundamental physical interaction, the only one that is rigorously present in all phenomena in nature, and always with an attractive behavior. A consistent Newtonian theory with varying G may suggest possible new relativistic structures, such as, for example, the non-minimal coupling of gravity with other fields, in a similar way as the general relativity equations suggested by the Poisson equation. We focus on the stellar structure of non-relativistic stars This is an important analysis in the context of the theory proposed in [10] since it has been shown that the main difference from the standard Newtonian gravity should manifest within matter distributions
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