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

**Sample text**

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.