General Relativity As an Aether Theory

TL;DR

This paper demonstrates that general relativity can be derived from an aether theory, combining Lorentz's and Kelvin's concepts, and offers a new perspective on Einstein's equations without relying on the covariant divergence condition.

Contribution

It provides a novel derivation of Einstein's equations using an aether framework, integrating Kelvin's aether theory with a generalized Cartan formalism.

Findings

Einstein equations derived from aether theory

Aether stress-energy tensor incorporated into Einstein equations

Generalized Cartan formalism allows spatial curvature in Newtonian gravity

Abstract

Most early twentieth century relativists --- Lorentz, Einstein, Eddington, for examples --- claimed that general relativity was merely a theory of the aether. We shall confirm this claim by deriving the Einstein equations using aether theory. We shall use a combination of Lorentz's and Kelvin's conception of the aether. Our derivation of the Einstein equations will not use the vanishing of the covariant divergence of the stress-energy tensor, but instead equate the Ricci tensor to the sum of the usual stress-energy tensor and a stress-energy tensor for the aether, a tensor based on Kelvin's aether theory. A crucial first step is generalizing the Cartan formalism of Newtonian gravity to allow spatial curvature, as conjectured by Gauss and Riemann.