Flat and Curved Space-times

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Oxford University Press, 2000 - Science - 375 pages
The present book explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasized throughout, and provides the basis of understanding of the special relativity effects of time dilation, length contraction, and the relativity of simultaneity. Bondi's K-calculus is introduced as a simple means of calculating the magnitudes of these effects, and leads to a derivation of the Lorentz transformation as a way of unifying these results. The invariant interval of flat space-time is generalised to that of curved space-times, and leads to an understanding of the basic properties of simple cosmological models and of the collapse of a star to form a black hole. The appendices enable the advanced student to master the application of four-tensors to the relativistic study of energy and momentum, and of electromagnetism. In addition, this new edition contains up-to-date information on black holes, gravitational collapse, and cosmology.
 

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Contents

Introduction
1
Fundamentals of measurement
35
i
44
The Lorentz transformation and the invariant interval
122
Curved spacetimes
196
Spherical and stellar collapse
237
Finale
313
B Fourvectors and relativistic dynamics
325
Fourvectors electromagnetism and energy
331
Symbols used
368
189
370
305
374
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About the author (2000)

G.F.R. Ellis, Professor of Mathematics, University of Cape Town, South Africa. R.M. Williams, Assistant Director of Research, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

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