2004arXiv (Cornell University)Open access

Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

Lee C. Loveridge

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Abstract

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

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Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

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Available abstract

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

Key concepts: Ricci decomposition, Riemann curvature tensor, Einstein tensor, Scalar curvature, Ricci curvature, Mathematical physics, Weyl tensor, Ricci flow

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