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Relativity, Gravitation and CosmologyA Basic Introduction$
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Ta-Pei Cheng

Print publication date: 2009

Print ISBN-13: 9780199573639

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199573639.001.0001

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Tensors in special relativity

Tensors in special relativity

(p.279) 12 Tensors in special relativity
Relativity, Gravitation and Cosmology

Ta-Pei Cheng

Oxford University Press

Tensors in a general coordinate system are introduced. When a tensor is expanded in terms of a set of basis (or inverse basis) vectors, the coefficients of expansion are its contravariant (or covariant) components with respect to this basis. The requirement of metric invariance in Minkowski spacetime leads to a generalized orthogonality condition, from which the Lorentz transformation can be derived. In terms of tensor we can have a manifestly covariant formalism. Maxwell's equations, the Lorentz force law, and the charge conservation equation are presented in their covariant forms. The symmetric energy-momentum tensor of a field system is introduced and the physical meaning of its components is discussed.

Keywords:   tensors in a general coordinate system, basis vectors, contravariant and covariant components, orthogonality condition, Lorentz transformation, Maxwell's equations, Lorentz force law, conservation, energy-momentum tensor

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