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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 Lorentzs and Kelvins 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 Kelvins aether theory. A crucial first step is generalizing the Cartan formalism of Newtonian gravity to allow spatial curvature, as conjectured by Gauss and Riemann.
This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations and discuss
The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action principle
We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the volume in
This is Chapter 1 in the book General Relativity and Gravitation: A Centennial Perspective, Edited by Abhay Ashtekar (Editor in Chief), Beverly Berger, James Isenberg, Malcolm MacCallum. Publisher: Cambridge University Press (June, 2015). It gives a
In this note we show that Newton-Schrodinger Equations (NSEs) [arXiv:1210.0457 and references therein] do not follow from general relativity (GR) and quantum field theory (QFT) by way of two considerations: 1) Taking the nonrelativistic limit of the