
Introduction  Table of Contents  Supplementary Material 
AMS/IP Studies in Advanced Mathematics 2009; 491 pp; hardcover Volume: 45 ISBN10: 0821848232 ISBN13: 9780821848234 List Price: US$119 Member Price: US$95.20 Order Code: AMSIP/45 See also: Advances in Lorentzian Geometry: Proceedings of the Lorentzian Geometry Conference in Berlin  Matthias Plaue, Alan Rendall and Mike Scherfner  This book consists of two independent works: Part I is "Solutions of the Einstein Vacuum Equations", by Lydia Bieri. Part II is "Solutions of the EinsteinMaxwell Equations", by Nina Zipser. A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of \(r\) and one less derivative than in the ChristodoulouKlainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the EinsteinMaxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the EinsteinMaxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field \(F\); in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of \(F\). In particular the Ricci curvature is a constant multiple of the stressenergy tensor for \(F\). Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field. Titles in this series are copublished with International Press, Cambridge, MA. Readership Graduate students and research mathematicians interested in general relativity. Reviews "Both parts are well written. ...the book should be of interest to anyone who is doing research in mathematical relativity."  Mathematical Reviews 


AMS Home 
Comments: webmaster@ams.org © Copyright 2014, American Mathematical Society Privacy Statement 