Abstract
The preceding chapter having introduced tensors on the vector space E underlying Minkowski spacetime \(\mathcal{E}\), we move now to the notion of tensor field, i.e. to the prescription of a tensor at each point of the affine space \(\mathcal{E}\). This chapter and the following one, dealing with the integration of tensor fields, are purely mathematical. They introduce the basic tools for the subsequent physical chapters devoted to electromagnetism, hydrodynamics and gravitation.
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Notes
- 1.
In Chap. 12, we have introduced, on a part of \(\mathcal{E}\), Rindler coordinates, which differ from affine coordinates.
- 2.
Vladimir A. Fock (1898–1974): Soviet theoretical physicist, known for his work in quantum mechanics (Fock space, Hartree–Fock approximation); he contributed also to geophysics and general relativity.
- 3.
In many textbooks, the vectors of this basis are denoted by \((\overrightarrow{\boldsymbol{e}}_{r},\overrightarrow{\boldsymbol{e}}_{\theta },\overrightarrow{\boldsymbol{e}}_{\varphi })\), while we reserve here this notation for the vectors of the coordinate basis.
- 4.
- 5.
Cf. Sect. 14.4 for the notations.
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Gourgoulhon, É. (2013). Fields on Spacetime. In: Special Relativity in General Frames. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37276-6_15
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