Chapter

Tensors in special relativity

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology

Second edition

Published in print November 2009 | ISBN: 9780199573639
Published online February 2010 | e-ISBN: 9780191722448 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199573639.003.0012

Series: Oxford Master Series in Physics

                      Tensors in special relativity

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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

Chapter.  10641 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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