HANS STEPHANI / DIETRICH KRAMER / MALCOLM MACCALLUM
CORNELIUS HOENSELAERS / AND EDUARD HERLT

Exact Solutions of Einstein's Field Equations
2nd Edition

Contents: 1. Introduction; Part I. General Methods: 2. Differential geometry without a metric; 3. Some topics in Riemannian geometry; 4. The Petrov classification; 5. Classification of the Ricci tensor; 6. Vector fields; 7. The Newman-Penrose and related formalisms; 8. Continuous goups of transformations; 9. Invariants and the characterization of geometries; 10. Generation techniques; Part II. Solutions with Groups of Motions: 11. Classification of solutions with isometries or homotheties; 12. Homogeneous space-times; 13. Hypersurface-homogeneous space-times; 14. Spatially-homogeneous perfect fluid cosmologies; 15. Groups G3 on non-null orbits V2; 16. Spherical symmetric perfect fluid solutions; 17. Groups G2 and G1 on non-null orbits; 18. Stationary gravitational fields; 19. Stationary axisymmetric fields: basic concepts; 20. Stationary axisymmetric vacuum solutions; 21. Non-empty stationary axisymmetric solutions; 22. Groups G2I on spacelike orbits I: Cylindrical symmetry; 23. Inhomogeneous fluid solutions with symmetry; 24. Groups on null orbits. Plane waves; 25. Collision of plane waves; Part III. Algebraically Special Solutions: 26. The various classes of algebraically special solutions; 27. The line element for k=s=0, Q+iw?0; 28. Robinson-Trautman solutions; 29. Twisting vacuum solutions; 30. Twisting Einstein-Maxwell and pure radiation fields; 31. Non-diverging solutions (Kundt’s class); 32. Kerr-Schild metrics; 33. Algebraically special perfect fluid solutions; Part IV. Special Methods: 34. Applications of generation techniques to General Relativity; 35. Special vector and tensor fields; 36. Solutions with special subspaces; 37. Embedding of four-dimensional Riemannian manifolds; Part V. Tables: 38. Introduction; References.

Essential Information
First Author: Stephani
Title: Exact Solutions of Einstein's Field Equations
ISBN, Binding, 0-521-46136-7 Hardback
Approximate Publication Date: c.01/04/2003
Main Subject Category: Theoretical, mathematical physics
Series: Cambridge Monographs on Mathematical Physics

Market (Subject)
physics (mathematical, theoretical), mathematics, relativity, cosmology, astrophysic, dynamical systems, differential geometry

Level
academic researchers, graduate students

Bibliographic Details
10 line diagrams 50 tables

Comparable titles: KRAMER et al./Exact Solutions of Einstein’s Equations/1981/0521 230411

C. ROGERS AND W. K. SCHIEF

Backlund and Darboux Transformations
Geometry and Modern Applications in Soliton Theory

Description: This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Backlund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Backlund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gaus-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Backlund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.

Contents: Preface; Acknowledgements; General introduction and outline; 1. Psudospherical surfaces and the Classical Backlund Transformation: the Bianchi system; 2. The motion of curves and surfaces. soliton connections; 3. Tzitzeica surfaces: conjugate nets and the Toda Lattice scheme; 4. Hasimoto Surfaces and the Nonlinear Schrodinger Equation. Geometry and Associated soliton Equations; 5. Isothermic surfaces: the Calapso and Zoomeron equations; 6. General aspects of soliton surfaces: role of gauge and reciprocal transfomations; 7. Backlund transformation and Darboux matrix connections; 8. Bianchi and Ernst systems. Backlund transformations and permutability theorems; 9. Projective-minimal and isothermal-asymptotic surfaces; A. The su(2)-so(3) isomorphism; B. CC-ideals; C. Biographies; Bibliography.

Essential Information
First Author: Rogers
Title: Backlund and Darboux Transformations
ISBN, Binding, 0-521-81331-X Hardback
ISBN, Binding, 0-521-01288-0 Paperback
Approximate Publication Date: c.01/08/2002
Main Subject Category: Applied mathematics, mathematical physics
Series: Cambridge Texts in Applied Mathematics, No. 30

Market (Subject)
applied mathematics, solitons, differential equations

Level
graduate students, academic researchers

Bibliographic Details
46 line diagrams 2 half-tones 76 exercises

Comparable titles: ALLDAY and PUPPE/Cohomological Methods in Transformation Groups/1993/0521 350220 KOSNIOWSKI/Transformation Groups/1977/0521 215099

JAMES R. WILSON AND GRANT J. MATHEWS

Relativistic Numerical Hydrodynamics

Description: Calculations of relativistic hydrodynamics are crucial to several areas of current research in the physics of supernovae and stellar collapse. This book provides an overview of the computational framework in which such calculations have been developed, with examples of applications to real physical systems. Beginning with the development of the equations and differencing schemes for special relativistic hydrodynamics, the book stresses the viability of the Euler -Lagrange approach to most astrophysical problems. It details aspects of solving the Einstein equations together with the fluid dynamics for various astrophysical systems in one, two and three dimensions. Summarizing much of the jargon and methods developed in the past thirty years, this book will be of great interest to graduate students and advanced researchers in relativistic astrophysics and cosmology.

Contents: 1. Introduction; 2. Special Relativistic Hydrodynamics; 3. General Relativistic Hydrodynamics; 4. (3+1) Cosmological Hydrodynamics; 5. Stellar Collapse and Supernovae; 6. Axially Symmetric Relativistic Hydrodynamics; 7. Conformally-Flat Hydrodynamics.

Essential Information
First Author: Wilson
Title: Relativistic Numerical Hydrodynamics
ISBN, Binding, 0-521-63155-6 Hardback
Approximate Publication Date: c.01/04/2003
Main Subject Category: Theoretical, mathematical physics
Series: Cambridge Monographs on Mathematical Physics

Market (Subject)
physics (theoretical), astrophysics

Level
graduate students, academic researchers

T. W. WRIGHT

The Physics and Mathematics of Adiabatic Shear Bands

Description: This book is a research monograph on the material instability known as adiabatic shear banding which often occurs in a plastically deforming material as it undergoes rapid shearing. Plastic deformation generates heat, which eventually softens most materials with continued straining, a process which is usually unstable. In this case the instability results in thin regions of highly deformed material, which are often the sites of further damage and complete failure. Divided into three parts, the book first reviews the physical phenomena and the standard methods of testing and characterization. It then establishes a general theory of isotropic plasticity with finite deformations as a setting for the simpler, but still nonlinear and highly coupled, equations of adiabatic shearing and the idealizations that are necessary to establish them. The main body of the book examines a series of one-dimensional problems of increasing complexity. In this way a comprehensive and quantitative picture of the complete phenomena is built up. Particular care is taken to use well established asymptotic techniques to find simple, but universal, analytic expressions or scaling laws that encapsulate various aspects of the dynamic formation and the final morphology of shear bands. The last two chapters review recent two-dimensional experiments and analyses. A fully developed mechanics of shear is just beginning to emerge as a major companion to fracture mechanics, this book may speed the process along.

Contents: Preface; 1. Introduction: Qualitative description and one dimensional experiments; 2. Balance laws and nonlinear elasticity: a brief summary; 3. Thermoplasticity; 4. Models for thermoviscoplasticity; 5. One-dimensional problems, part I: general considerations; 6. One-dimensional problems, part II. linearization and growth of perturbations; 7. One-dimensional problems, part III: nonlinear solutions; 8. Two-dimensional experiments; 9. Two-dimensional solutions.

Essential Information
First Author: Wright
Title: The Physics and Mathematics of Adiabatic Shear Bands
ISBN, Binding 0-521-63195-5 Hardback
Approximate Publication Date: c.01/08/2002
Main Subject Category: Applied mathematics, mathematical physics
Series: Cambridge Monographs on Mechanics

Market (Subject)
applied mathematics, materials science, mechanical engineering

Level
graduate students, academic researchers

Bibliographic Details
105 line diagrams

Comparable titles: TOWNSEND/Structure of Turbulent Shear Flow/1980/0521 298199/this is a fluids book, whereas Wright’s is a solids book, but the essence is the same

OLLE HAGGSTROM

Finite Markov Chains and Algorithmic Applications

Description: Based on a lecture course given at Chalmers University of Technology, this book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.

Contents: 1. Basics of probability theory; 2. Markov chains; 3. Computer simulation of Markov chains; 4. Irreducible and aperiodic Markov chains; 5. Stationary distributions; 6. Reversible Markov chains; 7. Markov chain Monte Carlo; 8. Fast convergence of MCMC algorithms; 9. Approximate counting; 10. Propp-Wilson algorithm; 11. Sandwiching; 12. Propp-Wilson with read once randomness; 13. Simulated annealing; 14. Further reading.

Essential Information
First Author: Haggstrom
Title: Finite Markov Chains and Algorithmic Applications
ISBN, Binding 0-521-81357-3 Hardback
ISBN, Binding 0-521-89001-2 Paperback
Approximate Publication Date: c.01/06/2002
Main Subject Category: Mathematics - analysis, probability
Series: London Mathematical Society Student Texts, No. 52

Market (Subject)
Markov chains, algorithmics

Level
graduate students, undergraduate students

Bibliographic Details
20 line diagrams

Comparable titles: MOTWANI/Randomised Algorithms/1995/0521 474655