By Mirjana Dalarsson, Nils Dalarsson
ISBN-10: 012200681X
ISBN-13: 9780122006814
This booklet combines relativity, astrophysics, and cosmology in one quantity, supplying an advent to every topic that allows scholars to appreciate extra specified treatises in addition to the present literature. The part on normal relativity provides the case for a curved space-time, offers the mathematical history (tensor calculus, Riemannian geometry), discusses the Einstein equation and its options (including black holes, Penrose techniques, and related topics), and considers the energy-momentum tensor for numerous ideas. the subsequent part on relativistic astrophysics discusses stellar contraction and cave in, neutron stars and their equations of country, black holes, and accretion onto collapsed gadgets. finally, the part on cosmology discusses numerous cosmological versions, observational assessments, and situations for the early universe. * in actual fact combines relativity, astrophysics, and cosmology in one quantity so scholars can comprehend extra designated treatises and present literature * wide introductions to every part are by means of proper examples and various workouts * offers an easy-to-understand method of this complex box of arithmetic and smooth physics by way of supplying hugely certain derivations of all equations and effects
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Extra info for Tensor calculus, relativity, and cosmology
Example text
20 THE EXPERIMENTAL BACKGROUND OF THE THEORY OF SPECIAL RELATIVITY The Michelson Morley Experiment The hypothesis advanced by Lorentz and by Fitzgerald was that all bodies are contractedin the direction of motion relative to the stationary ether by a factor VI — v2/c2. Again, let the ratio v/c be represented by the symbol /3, so that this factor may be written as V1 — /32. Now, if /° represents the length of a body at rest with respect to the ether (its rest length) and 1 its length when in motion with respect to the ether, then in the MichelsonMorley experiment - 11= /?
As for the origins of his special theory of relativity, Einstein was probably convinced, independently of the experimental background that we have presented, that Maxwell's equations had to have exactly the same form in all inertial * See Refs. 11-19 for some rewarding articles and books about Einstein. Q UESTIONS 31 frames of reference. He may have reached such a conclusion intuitively in his youth while meditating on how a light wave would look to an observer who was following it at speed c. The constancy of the velocity of light seemed to him indisputable, and his 1905 paper begins with the precise electrodynamical experimental situation described in a text on Maxwell's theory that he was studying at the time.
The "binumeral explosion" (one student's preference). (a) Use the binomial expansion theorem to verify each of the expansions displayed in the footnote on page 17. 30, what percent error is made in the first of these expansions if only two terms are kept? Only three terms? (c) Answer these same questions for the second of these expansions. * 18. Michelson Morley, generalized. Figure 1 11 shows a Michelson interferometer (compare Fig. 1-4) with a presumed ether wind whose uniform velocity v makes an - + 12) AN = /32(11 cos 20.