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Relativity, Tensors, and Curvature
2011Heuristics of Einstein's Theory What does g00 have to do with gravitation? The Metric Potentials Einstein's general theory of relativity is primarily a replacement for Newtonian gravitation and a generalization of special relativity. It cannot be “derived”; we can only speculate, with Einstein, by heuristic reasoning, how such a generalization ...
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2009
Abstract Differentiation of tensor components in a curved space must be handled with extra care. By adding another term (related to Christoffel symbols) to the ordinary derivative operator, we can form a “covariant derivative”; such a differentiation operation does not spoil the tensor property.
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Abstract Differentiation of tensor components in a curved space must be handled with extra care. By adding another term (related to Christoffel symbols) to the ordinary derivative operator, we can form a “covariant derivative”; such a differentiation operation does not spoil the tensor property.
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The Riemann tensor, the metric tensor, and curvature collineations in general relativity
Journal of Mathematical Physics, 1982The equation xμνRμ λαβ+xμλRμ ναβ = 0, where xμν and Rμ ναβ are the components of an arbitrary symmetric tensor and of the Riemann tensor formed from the metric tensor gμν, is trivially satisfied by xμν = φgμν. Nontrivial solutions are important in various areas of general relativity such as in the study of curvature collineations, and also in the study
McIntosh, C. B. G., Halford, W. D.
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General Relativity as an Attractor to Scalar-Tensor Gravity Theories
Astrophysics and Space Science, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mimoso, José P., Nunes, Ana
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Relative Moment Tensors Rejuvenated
We here present a recent approach to compute relative moment tensors for clustered seismicity tied to a reference moment tensor. It takes advantage of the similarity in subsurface Green’s functions for closely spaced events, facilitating accurate moment tensor calculations, especially for small earthquakes.Bloch, Wasja +4 more
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Tensor Formalism for General Relativity
2015Abstract This chapter introduces the basic tensor formalism needed for a proper formulation of general relativity. In a curved space, one must work with the covariant derivative, which is a combination of the ordinary derivative and the first derivatives of the metric (Christoffel symbols).
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Nonlocal Low-Rank Tensor Completion for Visual Data
IEEE Transactions on Cybernetics, 2021Lefei Zhang, Bo Du
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Guaranteed Tensor Recovery Fused Low-rankness and Smoothness
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023Hailin Wang +2 more
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