An introduction to semi-Riemannian geometry as a foundation for general relativity
Semi-Riemannian Geometry: The Mathematical Language of General Relativity (PDF) is an accessible exposition of the mathematics underlying general relativity. The ebook begins with background on linear and multilinear algebra, general topology, and real analysis. This is trailed by material on the classical theory of curves and surfaces, expanded to include both the Euclidean and Lorentz signatures. The remainder of the ebook is dedicated to a discussion of smooth manifolds, smooth manifolds with boundary, semi-Riemannian manifolds, smooth manifolds with a connection and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Numerous worked examples and detailed diagrams are provided to aid understanding. This ebook will appeal specifically to physics students wishing to learn more differential geometry than is usually offered in texts on general relativity.
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