Gravitation and Special Relativity

TL;DR

This paper presents a linear, relativistic field theory of gravity derived from Maxwell's equations, offering new insights into the structure of Einstein's equations and challenging traditional views on gravity's linearity.

Contribution

It introduces a Maxwell-like gravitational theory for weak fields, independent of Einstein's perturbation approach, and clarifies the energy-momentum tensor's role in cosmology.

Findings

Derives Maxwell-like equations for gravity

Shows gravity can be linear and relativistic in weak fields

Challenges traditional non-linear views of gravity

Abstract

A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way to a better understanding of the structure of the energy-momentum tensor in the Einstein Field Equations. Hence it is directly relevant to problems in modern cosmology. The derivation, independent of the perturbation theory of Einstein's equations, puts the gravitational and electromagnetic fields on an equal footing for weak fields, contrary to generally held views. The historical objections to a linear Lorentz invariant field theory of gravity are refuted for weak fields.