Semi-Riemannian Geometry With Applications to Relativity (Volume 103)

by Barrett O'Neill

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 Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Genres: Mathematics, Physics

488 pages, Hardcover

First published June 28, 1983

Reviews

[Matt · Rating 4 out of 5]

For the serious reader who wishes to continue on with a study of the Kerr solution to Einstein's equations, modeling the exterior spacetime of a rotating star.

[Jorge Ortiz · Rating 4 out of 5]

Why did you have to do it so difficult O'Neill??? The theory of semi-Riamnnian manifolds is beautiful, as well as powerfull, but the book is so rigorous that sometimes lacks the flesh in the bones. I don't think is a book for a first introduction into the subject, but a book that collects almost all the important results on it.

[Kibocchi · Rating 5 out of 5]

This book is meant for mathematicians that are used to precise definitions.

[Filip Dul · Rating 5 out of 5]

This is the preeminent mathematical text on general relativity. O’Neill beautifully conveys the inextricable relationship between modern geometry and why our rumps so strongly favor sitting over standing.