Malcolm MacCallum - Böcker

This book provides an introduction to the theory and application of the solution of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The theory and application of such methods have therefore attracted increasing attention in the last two decades. In this text the emphasis is on how to find and use the symmetries in different cases. Many examples are discussed, and the book includes more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book an invaluable reference.

A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.