By Hans Stephani
ISBN-10: 0511186274
ISBN-13: 9780511186271
ISBN-10: 0511187203
ISBN-13: 9780511187209
ISBN-10: 051164809X
ISBN-13: 9780511648090
ISBN-10: 0521010691
ISBN-13: 9780521010696
ISBN-10: 0521811856
ISBN-13: 9780521811859
Completely revised and up-to-date, this self-contained textbook offers a pedagogical creation to relativity. It covers an important beneficial properties of unique in addition to basic relativity, and considers tougher issues, comparable to charged pole-dipole debris, Petrov class, teams of motions, gravitational lenses, certain suggestions and the constitution of infinity. the required mathematical instruments are supplied, such a lot derivations are entire, and workouts are integrated the place applicable. The bibliography lists the unique papers and in addition directs the reader to worthwhile monographs and assessment papers. earlier variation Hb(1990): 0-521-37066-3 past version Pb(1990): 0-521-37941-5
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Extra info for Relativity : an introduction to special and general relativity
Example text
14) with δ = π/2 − α . Show that a motion of the mirror in its plane does affect the reflection angles and the frequencies. A rocket flies through a large ring (radius R) orthogonal to its orbit. How far back is the plane of the ring with respect to the rocket when the pilot sees it as exactly to his left? 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.
3) Examples of scalars are the rest mass m0 , the proper time τ, and the phase Φ of a wave. Four-vectors, or tensors of rank 1, are objects with four components which transform as the components of xn , an = Ln m am , a m = Lm n a n . 4) Examples are the force f n , the four-velocity un , and the wave vector k n . Indices can be raised, or lowered, with the help of the matrix η, an = ηnm am , an = η nm am , η nm = diag (1, 1, 1, −1) = ηnm , ηnm = δnm . 5) The an are called the contravariant, and the an the covariant components of the vector.
A rocket flies through a large ring (radius R) orthogonal to its orbit. How far back is the plane of the ring with respect to the rocket when the pilot sees it as exactly to his left? 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.