General Relativity: With Applications to Astrophysics

ISBN-13: 9783642060137 / Angielski / Miękka / 2010 / 676 str.

Norbert Straumann

Opis

Physics and mathematics students are as eager as ever to become acquainted withthefoundationsofgeneralrelativityandsomeofitsmajorapplicationsin astrophysics and cosmology. I hope that this textbook gives a comprehensive and timelyintroduction toboth aspectsof thisfascinating?eld, and willturn out to be useful for undergraduate and graduate students. This book is a complete revision and extension of my previous volume GeneralRelativityandRelativisticAstrophysics thatappearedabouttwenty years ago in the Springer Series Texts and Monographs in Physics; however, it cannot be regarded just as a new edition. In Part I the foundations of general relativity are thoroughly developed. Some of the more advanced topics, such as the section on the initial value problem, can be skipped in a ?rst reading. Part II is devoted to tests of general relativity and many of its app- cations. Binary pulsars our best laboratories for general relativity are studied in considerable detail. I have included an introduction to gravi- tional lensing theory, to the extend that the current literature on the subject should become accessible. Much space is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel s proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten s proof of the positive energy theorem. All the required di?erential geometric tools are developed in Part III."

Recenzje

From the reviews:

"In this book Norbert Straumann presents a pedagogically precise and highly informative account of both the physical and advanced mathematical concepts that a professional working in this field requires. The essential differential geometry background is placed in an extensive part ... . the treatment is both physically rigorous and comprehensive. This book is an important acquisition for anyone working in this area." (Geoffrey Bicknell, Australian Physics, Vol. 42 (4), September/October, 2005)

"This text provides a comprehensive and timely introduction to general relativity. ... The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for strong theory and other fields of physics, classical as well as quantum." (ETDE Energy Database Energiedatenbank, November, 2004)

"From the earliest sections, Straumann makes absolutely no pretence that this is a beginner's guide to general relativity ... . There are points of interest for those disinclined (or unable) to follow the maths in detail. ... this book is primarily aimed at those who want to get very, very intimate with the mathematics of general relativity in an astrophysical .... context and who are endowed with a considerable background in all three subjects. ... this may be the ultimate specialist textbook." (Roger Feasey, Journal of the Auckland Astronomical Society, 2005)

Spis treści

1 Physics in External Gravitational Fields.- 2 Einstein’s Field Equations.- 3 The Schwarzschild Solution and Classical Tests of General Relativity.- 4 Weak Gravitational Fields.- 5 The Post-Newtonian Approximation.- 6 White Dwarfs and Neutron Stars.- 7 Black Holes.- 8 The Positive Mass Theorem.- 9 Differentiable Manifolds.- 10 Tangent Vectors, Vector and Tensor Fields.- 11 The Lie Derivative.- 12 Differential Forms.- 13 Affine Connections.- 14 Some Details.- A Fundamental Equations for Hypersurfaces.- B Ricci Curvature of Warped Products.- C Frobenius Integrability Theorem.- D Collection of Important Formulas.- References.

Blurb

This text provides a comprehensive and timely introduction to general relativity. The foundations of the theory in Part I are thoroughly developed together with the required mathematical background from differential geometry in Part III. The six chapters in Part II are devoted to tests of general relativity and to many of its applications. Binary pulsars are studied in considerable detail. Much space is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and derivations of the basic laws of black hole physics. The final chapter of this part contains Witten's proof of the positive energy theorem.

The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for string theory and other fields of physics, classical as well as quantum.