Semi-Riemannian Geometry With Applications to Relativity

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)—the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical...