This text explains special relativity and the foundations of general relativity theory in terms understandable to undergraduates in mathematics and physics coming to the subject for the first time. Space-time geometry is emphasized throughout, providing a basic 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 this leads to a derivation of the Lorentz Transformation as a way of unifying these results. The invariant interval of flat space-time is compared to that of curved space-times, and the basic properties of simple cosmological models are presented. Appendices enable the advanced student to master the application of four tensors to the relativistic study of energy, momentum and electromagnetism.
George Francis Rayner Ellis, FRS, Hon. FRSSAf, is the Emeritus Distinguished Professor of Complex Systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa.
He is considered one of the world's leading theorists in cosmology. He is an active Quaker and in 2004 he won the Templeton Prize. On 18 May 2007, he was elected a Fellow of the British Royal Society.
From 1989 to 1992 he served as President of the International Society on General Relativity and Gravitation. He is a past President of the International Society for Science and Religion. He is an A-rated researcher with the NRF.