2020/04/07 by Géry de Saxcé, de Saxcé, Géry
Physics and Astronomy · #83C25 (Primary) 70G45 (Secondary) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.2004.03513
openalex publication_date 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Galilean gravitation derives from a scalar potential and a vector one. Poisson's equation to determine the scalar potential has no the expected Galilean covariance. Moreover, there are three missing equations to determine the potential vector. Besides, we require they have the Galilean covariance. These are the issues addressed in the paper. To avoid the drawbacks of the PPN approach and the NCT, we merge them into a new framework. The key idea is to take care that every term of the c expansion of the fields are Galilean covariants or invariants. The expected equations are deduced by variation of the Hilbert-Einstein functional. The contribution of the matter to the functional is derived from Souriau's conformation tensor. We obtain a system of four non linear equations, solved by asymptotic expansion.