Titlebook: Special Relativity in General Frames; From Particles to As Éric Gourgoulhon Textbook 2013 Springer-Verlag Berlin Heidelberg 2013 Limits of

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Angular Momentum, is first defined, together with the angular momentum vector relative to an observer. The definition is then extended to a particle system, and the angular momentum 2-form is decomposed in terms of the angular momentum vector and the mass-energy dipole moment. The principle of angular momentum conse

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Principle of Least Action,irst discussed. The principle of least action is stated, and the Euler–Lagrange equations are derived. The specific cases of a free particle and a particle in scalar, vector or second-rank tensor fields are treated. The Noether theorem is presented. The generalized four-momentum and the Hamiltonian

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catagen

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Tensors and Alternate Forms,ms encountered in the previous chapters. After the definition of tensors, basic operations on them are considered: tensor product, contraction and expansion with respect to a vector basis. The specific case of alternate forms is then discussed in detail, with the associated operations of exterior pr

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Fields on Spacetime,escription of a tensor at each point of the affine space .. 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.