This unique monograph by a noted UCLA professor examines in detail the mathematics of Kerr black holes, which possess the properties of mass and angular momentum but carry no electrical charge. Suitable for advanced undergraduates and graduate students of mathematics, physics, and astronomy as well as professional physicists, the self-contained treatment constitutes an introduction to modern techniques in differential geometry. The text begins with a substantial chapter offering background on the mathematics needed for the rest of the book. Subsequent chapters emphasize physical interpretations of geometric properties such as curvature, geodesics, isometries, totally geodesic submanifolds, and topological structure. Further investigations cover relativistic concepts such as causality, Petrov types, optical scalars, and the Goldberg-Sachs theorem. Four helpful appendixes supplement the text.
About the Author
Barrett O'Neill (1924-2011) was Professor of Mathematics at UCLA from 1951 until his retirement in 1991. In addition to this volume, he was the author of two other distinguished books, Elementary Differential Geometry and Semi-Riemannian Geometry.