Flat and Curved Space-Times [Paperback]

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.

Introduction
1. Space-time diagrams and the foundations of special relativity
2. Fundamentals of measurement
3. Measurements in flat space-times
4. The Lorentz transformation and the invariant interval
5. Curved space-times
6. Spherical and stellar collapse
7. Simple cosmological models
8. Finale
Afterword
Appendix A. Line integrals
Appendix B. Four-vectors and relativistic dynamics
Appendix C. Four-vectors, electromagnetism, and energy-momentum conservation
Symbols used
Index