Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.
Table of Contents
Introduction - Riemannian themes in Lorentzian geometry; connections and curvature; Lorentzian manifolds and causality; Lorentzian distance; examples of space-times; completness and extendibility; stability of completeness and incompleteness; maximal geodesics and causally disconnected space-times; the Lorentzian cut locus; Morse index theory on Lorentzian manifolds; some results in global Lorentzian geometry; singularities; gravitational plane wave space-times; the splitting problem in global Lorentzian geometry. Appendices: Jacobi Fields and Toponogov's theorem for Lorentzian manifolds; from the Jacobi, to a Riccati, to the Raychaudhuri equation - Jacobi Tensor Fields and the exponential map revisited.
"Praise for the previous edition. . . The global theory of Lorentzian geometry has grown up, during the last twenty years, and. . .[the authors] have given us an authoritative and highly readable treatment of the subject as it stands today. "
---Bulletin of the American Mathematical Society
". . .an ambitious and welcome compendium of research in the field. The authors have demonstrated command of the literature and presented it with care. They write well, effectively exploiting the comparisons and contrasts to produce a readable text. "
---Mathematical Reviews . . .and for the Second. . .
"By substantially updating the material of the first edition, the authors have guaranteed that their book will assume in the contemporary literature the position it held upon its first appearance. . . . . .anyone interested in pseudo-Riemannian geometry and/or general relativity will find this new edition both timely and valuable. "
"The enormous interest for spacetime differential geometry, especially with respect to its applications in general relativity, has prompted the authors to add new material reflecting the best achievements in the field. . . .a most valuable reference for anyone interested in global Lorentzian geometry….the selfcontained character of this book and the excellent organization of the material make it a perfect source for a graduate course. "