We propose a Lagrangian formulation for a varying G Newtonian-like theory inspired by the Brans–Dicke gravity. Rather than imposing an ad hoc dependence for the gravitational coupling, as previously done in the literature, in our proposal, the running of G emerges naturally from the internal dynamical structure of the theory. We explore the features of the resulting gravitational field for static and spherically symmetric mass distributions as well as within the cosmological framework.
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We dedicate this work to the memory of Antonio Brasil Batista, one the founders of the research group Cosmo-ufes, who has introduced us to the problem of the variation of the gravitational coupling in newtonian and relativistic theories. We thank Davi C. Rodrigues for enlightening discussions on the subject of this paper. JCF thanks CNPq and FAPES for partial financial support. HV thanks CNPq and PROPP/UFOP for partial financial support. JDT thanks FAPES and CAPES for their support through the Profix program. TG thanks FAPES for their support.
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Fabris, J.C., Gomes, T., Toniato, J.D. et al. Newtonian-like gravity with variable G. Eur. Phys. J. Plus 136, 143 (2021). https://doi.org/10.1140/epjp/s13360-021-01146-z