Relativity : an introduction to special and general by Hans Stephani

By Hans Stephani

Completely revised and up-to-date, this self-contained textbook offers a pedagogical advent to relativity. It covers crucial good points of targeted in addition to common relativity, and considers more challenging subject matters, corresponding to charged pole-dipole debris, Petrov category, teams of motions, gravitational lenses, designated ideas and the constitution of infinity. the required mathematical instruments are supplied, such a lot derivations are entire, and workouts are integrated the place acceptable. The bibliography lists the unique papers and in addition directs the reader to precious monographs and evaluate papers. past version Hb(1990): 0-521-37066-3 past variation Pb(1990): 0-521-37941-5

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Relativity : an introduction to special and general relativity

Completely revised and up-to-date, this self-contained textbook offers a pedagogical advent to relativity. It covers crucial gains of distinctive in addition to common relativity, and considers more challenging issues, corresponding to charged pole-dipole debris, Petrov class, teams of motions, gravitational lenses, specified options and the constitution of infinity.

Extra resources for Relativity : an introduction to special and general relativity

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We therefore can assume vA = vB for all particles participating in the process, and moreover FAB = −FBA . 26), we conclude that 32 Mechanics of Special Relativity p2 2 1 ϕ2 2 Σ p2 p1 ϕ1 1 Σ p1 Fig. 6. Elastic collision of two particles. , A mA c = A EA /c = const. 28) or Pn ≡ A pnA = const. 29) holds: three-momentum and energy, or four-momentum, are conserved. 1. So there is a coordinate system in which it has the normal form P n = (0, P 4 ). 30) This system is called the centre of mass system.

6) which for all xa is possible only if Ln a Ln b = δab , a, b, n = 1, . . , 4. 7) These equations define the Lorentz transformations, first given by Waldemar Voigt (1887). The discussion of these transformations will fill the next chapters of this book. 8) we obtain the Poincar´e transformations. 13) for rotations, D v α Dν β = δαβ , to which it reduces when the time (the fourth coordinate) is kept fixed: Dν α 0 Ln a = . 9) 0 1 Rotations leave xα xα = x2 + y 2 + z 2 invariant, Lorentz transformations xa xa = x2 + y 2 + z 2 − c2 t2 .

6 Four-dimensional vectors and tensors Before we can treat Electrodynamics and Fluid Mechanics, we need some more tools from tensor algebra and analysis which we will supply now. We shall do that in some detail, since they are very similar to those used in General Relativity. 1 Some definitions We repeat and list here the basic definitions, with only short comments. 1) which satisfy Lm b = ηm n η ab Ln a , Ln a Lm a n = δm . 2) Scalars, or tensors of rank 0, are functions ϕ which remain invariant under Lorentz transformations, 42 Four-dimensional vectors and tensors ϕ = ϕ.

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