Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation

TL;DR

This paper develops a scalar ether theory of gravitation where gravity is a pressure force, deriving continuum dynamics and modified Maxwell equations that are consistent with photon behavior but challenge local charge conservation.

Contribution

It introduces a novel scalar gravitation theory based on pressure forces, extending continuum dynamics and deriving modified Maxwell equations compatible with photon optics.

Findings

Maxwell equations are modified under the scalar gravity theory.

The theory predicts non-conservation of charge in variable gravitational fields.

Photon dynamics are consistent with the geometrical optics approximation.

Abstract

An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton's second law. This implies Einstein's geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell's equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a "free" photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field. Keywords: Alternative theories of gravitation; preferred reference frame; curved spacetime; Maxwell equations; charge conservation