Flat and Curved Space-times

An explanation of special relativity and the foundations of general relativity theory from a geometric viewpoint with emphasis on space-time geometry throughout.

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An explanation of special relativity and the foundations of general relativity theory 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 generalized 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. Appendices enable the advanced student to master the application of 4 tensors to the relativistic study of energy and momentum, and of electromagnetism.