A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity

Einstein’s theories of special and general relativity together form a cornerstone of modern physics. Based on the notion of curved, four-dimensional spacetime, relativity helps to explain phenomena as diverse as time dilation, length contraction, mass-energy equivalence, the formation of black holes and the evolution of the Universe. Using clear and accessible language, and with numerous fully solved problems, this self-study guide is aimed at the general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. For those with minimal mathematical background, the first chapter provides a crash course in elementary mathematics. The reader is then taken gently by the hand and guided through a wide range of topics including Newtonian mechanics, the Lorentz transformations, tensor calculus, the Schwarzschild solution, simple black holes and Friedmann-Robertson-Walker cosmological models. Understand even the basics of Einstein's amazing theory and the world will never seem the same again.