Newtonian Gravitational Waves from a Continuum

TL;DR

This paper demonstrates that Newtonian dynamics for continuous mass distributions can produce gravity waves propagating at finite speed, showing an electromagnetic-like behavior and Lorentz invariance within a Newtonian framework.

Contribution

It establishes an equivalence between Newtonian fluid equations and Maxwell-like equations, revealing gravity waves and finite propagation speed in Newtonian gravity.

Findings

Gravity waves propagate at finite speed similar to electromagnetic waves.

Newtonian gravitation equations exhibit Lorentz invariance.

Continuous mass distributions can generate gravity waves in Newtonian physics.

Abstract

Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e g compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i e the inviscid Navier Stokes equations for a general variable gravitational field g(t,x), are equivalent to a form identical to Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at finite speed. The latter implies that Newtonian gravitation as presented in this paper is not spooky action at a distance but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that in analogy to Maxwell equations the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light.