Newtonian Gravitational Radiation and Waves

Gustavo V López

doi:10.4236/jamp.2020.88110

Abstract

In this paper, we review historical Maxwell's equation for gravity and recent studies on the lack of curvature of linear dipole gravitational waves. The extended Newton's gravity necessarily has the continuity equation for the conservation of mass, and with the Gauss' equation associated to gravitational time depending field R, bring about a new field W which resembles the magnetic field in Electrodynamics. Although this field has not been found yet, its existence comes from a strong mathematical statement, and it is shown that linear dipole gravitational waves have their origin in extended Newton theory of gravity. This is a direct mathematical consequence of Gauss' law and the continuity equation for the density of mass and current, and as a direct result of this, any accelerated mass will emit mainly dipole gravitational radiation. Then, one concludes that dipole gravitational waves can have its origin on the extended Newton's gravity equations.

Highlights

It was shown that Maxwell’s equations for gravitational field appear without having any relation at all with General Relativity or space-time curved. This is just due to Gauss’ theorem and the continuity equation for density of mass and current which allowed to have the existence of a new gravitational field W, with similar properties properties to the magnetic field in Electrodynamics
Experimental verification of the existence of this new gravitational field is required, its mathematical existence is out of question. It is absolutely astonishing the existing closely relation between post Newtonian gravity theory and Electrodynamics theory, indicating that a space-time curved is not needed for the description of linear dipole gravitational waves
Non-linear and some linear gravitational waves are described by general relativity

Summary

Maxwell’s Equation for Gravity

Λ λ ∂t where λ is the speed of gravity propagation, and J is the density of current (G ≈ 6.674 × 10−11 m3/Kg · s2 is the gravitational constant). Given ρ and J, the resulting decoupled equations for R and W are the inhomogeneous wave equations. Lopez where one can see the λ is effectively the speed of gravity propagation. As in ordinary Maxwell’s equation for electrodynamics, the fields R and W can be written in terms of an scalar potential Φ and vector potential A as 1 ∂A. Λ ∂t and with the usual Lorentz’ norm ( ∇ · A + ∂Φ/∂λt=0), one gets that Φ and A satisfy inhomogeneous wave equations. The Poyting vector S and the density of gravitational energy ug are well defined quantities given by λ.

Newtonian Gravitational Waves

Conclusion and Comments