**Authors**: Mathieu Beau (STP-DIAS)

**Date**: 4 Sep 2012

**Abstract**: We propose a vectorial field theory (G) based on a so-called \textit{gravitational induction principle} saying that a density current of accelerated particles generate a vectorial field $G_\mu$. The aim of this article is to give a first approach of this theory. We fist construct a Lagrangian $L_G=-mcˆ2 G_\mu(x)\ddot{x}ˆ\mu$ (where $m$ is the mass of the particle, $\ddot{x}ˆ\mu$ its acceleration) analogous to the electrodynamic Lagrangian $L_{ED}=-q A_\mu(x)\dot{x}ˆ\mu$ (where $q$ is the charge of the particle, $\dot{x}ˆ\mu$ its velocity) and then we give the analogous field equations based on the induction principle. Using these field equations, we establish new kind of gravitomagnetic equations (GEM-G) valid for small velocities, analogous to the gravitomagnetic field equation (GEM) proved by the general theory of the relativity (RG). Then, we will propose a first approach about the description of the vectorial field theory (G) in the framework of the general relativity theory (RG), we will give the field equations and we will discuss the conceptual consequences of a theory of gravitation with both different fields.

1209.0611
(/preprints)

2012-09-17, 13:39
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*