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Lagrangian Extensions of Newtonian Gravity constrained by Solar System tests

arXiv Physics Thursday 04 June 2026, 04:00 UTC By Pedro H. Dalpr\'a, J\'ulio C. Fabris, Hermano Velten, J\'unior D. Toniato 1 min read
Key Points

Announce Type: cross Abstract: We explore an extension to Newtonian gravity through a generalised Lagrangian function with the introduction of a second dynamical scalar field. Building on previous research into gravity with variable gravitational coupling, the work derives the complete field equations and applies a weak-field approximation. This leads to an effective post-Newtonian gravitational potential that includes key aspects of relativistic theories.

arXiv:2606.04077v1 Announce Type: cross Abstract: We explore an extension to Newtonian gravity through a generalised Lagrangian function with the introduction of a second dynamical scalar field. Building on previous research into gravity with variable gravitational coupling, the work derives the complete field equations and applies a weak-field approximation. This leads to an effective post-Newtonian gravitational potential that includes key aspects of relativistic theories. The resulting N-body equations of motion highlight differences among inertial and gravitational masses, which can constrain the theory's free parameter through data from the Nordtvedt effect. By employing the method of osculating orbits for a two-body system, the study calculates the secular variation of the orbital pericenter and aligns this with the latest data on Mercury's perihelion shift, for another observational constraint on the model. Furthermore, a few examples of theories are discussed.
Lagrangian Extensions of Newtonian Gravity (ORG) Solar System (ORG) Newtonian (ORG) Lagrangian (ORG) Nordtvedt (PERSON) Mercury (ORG)
Originally published by arXiv Physics Read original →

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