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First Course in General Relativity 3rd Revised edition [Kietas viršelis]

4.17/5 (533 ratings by Goodreads)
(Cardiff University)
  • Formatas: Hardback, 512 pages, aukštis x plotis x storis: 253x196x28 mm, weight: 1260 g, Worked examples or Exercises
  • Išleidimo metai: 30-Jun-2022
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1108492673
  • ISBN-13: 9781108492676
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 512 pages, aukštis x plotis x storis: 253x196x28 mm, weight: 1260 g, Worked examples or Exercises
  • Išleidimo metai: 30-Jun-2022
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1108492673
  • ISBN-13: 9781108492676
Kitos knygos pagal šią temą:
"Clarity, readability and rigor combine in the third edition of this widely used textbook to provide the first step into general relativity for advanced undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysics researchers and students alike are covered with Schutz's characteristic ease and authority, from black holes to relativistic objects, from pulsars to the study of the Universe as a whole. This third edition contains discoveries by astronomers that require general relativity for their explanation; two chapters on gravitational waves, including direct detections of gravitational waves and the impact of their observation on cosmological measurements; new information on black holes and neutron stars; and greater insight into the expansion of the Universe. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, while the informal writing style and worked examplesmake the subject matter easily accessible"--

Recenzijos

Praise for the second edition: 'Bernard Schutz's textbook A First Course in General Relativity quickly became a classic, notable for its use of the geometrical approach to the subject, combined with a refreshing succinctness. Since its first publication in 1985, the field of general relativity has exploded Schutz has done a masterful job of incorporating these new developments into a revised edition, which is sure to become a new 'classic'.' Clifford M. Will, McDonnell Center for the Space Sciences, Washington University, St. Louis Praise for the second edition: 'This new edition retains all of the original's clarity and insight into the mathematical foundations of general relativity, but thoroughly updates the accounts of the application of the theory in astrophysics and cosmology. The result is an indispensable volume and this new edition will no doubt become a classic text in its own right.' Mike Hobson, Cavendish Laboratory, University of Cambridge Praise for the second edition: 'Schutz has updated his eminently readable and eminently teachable A First Course in General Relativity. This text will be appreciated by any upper-level undergraduate with an interest in cosmology, astrophysics, or experimentation in gravitational physics.' Richard Matzner, The Center for Relativity, University of Texas at Austin Praise for the second edition: ' marvellous very clear I cannot recommend this book highly enough to any physicist who wants a good introduction to general relativity.' David Burton, The Observatory Praise for the first edition: 'Schutz has such mastery of the material that it soon becomes clear that one is in authoritative hands, and topics are selected and developed only to a point where they prove adequate for future needs.' The Times Higher Education Supplement Praise for the first edition: ' ought to inspire more physicists and astronomers to teach and learn the other half of the twentieth century's revolution in physics.' Foundations of Physics Praise for the first edition: 'The book is a goldmine of cleverly constructed problems and exercises (and solutions!).' Nature Praise for the first edition: ' provides the first step into general relativity for undergraduate students with a minimal background in mathematics.' Zentralblatt MATH 'Several generations of students have benefitted from the first two editions of Professor Bernard Schutz' beautiful introductory textbook on tensor algebra, manifolds, physics in curved space times, and Einstein's field equations. Why another edition now? The answer is that, in the last years, precision measurements of stellar orbits around the central massive black hole in the Galactic Center, the detection of gravitational waves from in-spiraling binary black holes and neutron stars with LIGO, and the detection of the central 'radio wave shadow' of the supermassive black hole in the galaxy M87 have suddenly opened the magical world of strongly curved spacetime to precision experimental tests. These experiments and much more to come from ground- and space-based gravitational wave studies have started a renaissance of interest in Einstein's theory.' Reinhard Genzel, Max Planck Institute for Extraterrestrial Physics 'Students and teachers of general relativity will welcome this new edition of Schutz' hugely popular text, significantly broadened to cover the astonishing discoveries of gravitational-wave astronomy and their implications. A pioneer of the geometrical approach to undergraduate-level teaching of GR, the book remains unmatched in its highly readable style. With vim and authority, Schutz leads his readers masterfully from mathematical foundations to the forefront of research in astronomy and cosmology, providing them with the tools to understand future discoveries. With this new edition, Schutz' classic text remains as fresh and relevant as ever.' Leor Barack, University of Southampton 'An outstanding textbook on general relativity written with the author's customary clarity and in his engaging style. It includes not only the basics of general relativity, but also recent developments in the direct detection of gravitational waves. A clear exposition of the essential ideas and methods.' Rong-Gen Cai, Chinese Academy of Sciences 'Professor Schutz' informal style bewitches the reader into absorbing profound and complex concepts effortlessly. Physics is explained in a lucid style with minimal mathematics, without compromising on rigour. The recent excitement in the field of gravitational waves and its implications for astronomy and cosmology is adeptly conveyed. This edition has been enriched with several more exercises which the student or the young researcher will find illuminating and instructive.' Sanjeev Dhurandhar, Inter University Centre for Astronomy and Astrophysics 'When I first taught from this book in the 1980s, my students and I loved it for its unusual combination of clarity and brevity. This third edition is not quite as brief because so much has happened in the subject! But for an all-around text with clear writing and an engaging style, it is still top of the class.' Clifford Will, University of Florida 'A First Course in General Relativity by Bernard Schutz is an outstanding introductory text on Einstein's theory of general relativity and offers an invaluable resource for students interested in understanding the formal and physical foundations of modern spacetime theory.' Karim Thebault, University of Bristol 'As with its previous editions, this textbook provides a fantastically accessible introduction to the key physical concepts of general relativity and the formalism used by its practitioners. The third edition gives a much-needed update accounting for discoveries since the previous edition, with the chapters on gravitational waves in particular serving as outstanding tutorials for students who are interested in astronomical applications of this subject.' Scott Hughes, Massachusetts Institute of Technology

Daugiau informacijos

This widely used textbook explains general relativity for advanced undergraduates, requiring only a minimal background in mathematics.
Preface to the third edition ix
Preface to the second edition xi
Preface to the first edition xiii
1 Special relativity
1(32)
1.1 Fundamental principles of special relativity theory (SR)
1(2)
1.2 Definition of an inertial observer in SR
3(1)
1.3 New units
4(1)
1.4 Spacetime diagrams
5(1)
1.5 Construction of the coordinates used by another observer
6(3)
1.6 Invariance of the interval
9(4)
1.7 Invariant hyperbolae
13(4)
1.8 Particularly important results
17(4)
1.9 The Lorentz transformation
21(2)
1.10 The velocity-addition law
23(1)
1.11 Paradoxes and physical intuition
23(1)
1.12 Bibliography
24(1)
1.13 Appendix: The twin `paradox' dissected
25(8)
Exercises
27(6)
2 Vector analysis in special relativity
33(23)
2.1 Definition of a vector
33(3)
2.2 Vector algebra
36(5)
2.3 The four-velocity
41(1)
2.4 The four-momentum and its conservation
42(2)
2.5 Scalar product
44(2)
2.6 Applications
46(2)
2.7 Photons
48(1)
2.8 Bibliography
49(7)
Exercises
50(6)
3 Tensor analysis in special relativity
56(28)
3.1 The metric tensor
56(1)
3.2 Definition of tensors
56(2)
3.3 The (0/1) tensors: one-forms
58(4)
3.4 Gradient of a function is a one-form
62(4)
3.5 The (0/2) tensors
66(2)
3.6 Metric as a mapping of vectors into one-forms
68(4)
3.7 Finally: (M/N) tensors
72(1)
3.8 Index `raising' and `lowering'
73(2)
3.9 Differentiation of tensors
75(1)
3.10 Bibliography
76(8)
Exercises
76(8)
4 Perfect fluids in special relativity
84(27)
4.1 Fluids
84(1)
4.2 Dust: the number-flux vector N
85(3)
4.3 One-forms and surfaces
88(3)
4.4 Dust again: the stress-energy tensor
91(2)
4.5 General fluids
93(5)
4.6 Conservation of energy-momentum
98(2)
4.7 Perfect fluids
100(3)
4.8 Importance for general relativity
103(1)
4.9 Gauss' law
104(2)
4.10 Bibliography
106(5)
Exercises
106(5)
5 Preface to curvature
111(30)
5.1 On the relation of gravitation to curvature
111(7)
5.2 Tensor algebra in polar coordinates
118(6)
5.3 Tensor calculus in polar coordinates
124(6)
5.4 Christoffel symbols and the metric
130(4)
5.5 Noncoordinate bases
134(4)
5.6 Looking ahead
138(1)
5.7 Bibliography
138(3)
Exercises
138(3)
6 Curved manifolds
141(29)
6.1 Differentiable manifolds and tensors
141(2)
6.2 Riemannian manifolds
143(6)
6.3 Covariant differentiation on a general manifold
149(3)
6.4 Parallel transport, geodesies, and curvature
152(4)
6.5 The curvature tensor
156(6)
6.6 Bianchi identities; Ricci and Einstein tensors
162(2)
6.7 Curvature in perspective
164(1)
6.8 Bibliography
165(5)
Exercises
165(5)
7 Physics in a curved spacetime
170(13)
7.1 The transition from differential geometry to gravity
170(4)
7.2 Physics in slightly curved spacetimes
174(2)
7.3 Curved intuition
176(1)
7.4 Conserved quantities
177(3)
7.5 Bibliography
180(3)
Exercises
180(3)
8 The Einstein field equations
183(19)
8.1 Purpose and justification of the field equations
183(3)
8.2 Einstein's equations
186(2)
8.3 Einstein's equations for weak gravitational fields
188(4)
8.4 Newtonian gravitational fields
192(4)
8.5 Bibliography
196(6)
Exercises
197(5)
9 Fundamentals of gravitational radiation
202(65)
9.1 The role of general relativity in the physical Universe
202(1)
9.2 The propagation of gravitational waves
203(10)
9.3 The detection of gravitational waves
213(17)
9.4 The generation of gravitational waves
230(9)
9.5 The energy carried away by gravitational waves
239(8)
9.6 Standard sirens
247(6)
9.7 Bibliography
253(14)
Exercises
255(12)
10 Spherical solutions for stars
267(29)
10.1 Coordinates for spherically symmetric spacetimes
267(2)
10.2 Static spherically symmetric spacetimes
269(2)
10.3 Static perfect-fluid Einstein equations
271(2)
10.4 The exterior geometry
273(1)
10.5 The interior structure of the star
274(2)
10.6 Exact interior solutions
276(4)
10.7 Realistic stars and gravitational collapse
280(11)
10.8 Bibliography
291(5)
Exercises
292(4)
11 Schwarzschild geometry and black holes
296(64)
11.1 Trajectories in the Schwarzschild spacetime
296(19)
11.2 Nature of the surface r = 2M
315(7)
11.3 General black holes
322(15)
11.4 Real black holes in astronomy
337(8)
11.5 Hawking radiation
345(5)
11.6 Bibliography
350(10)
Exercises
352(8)
12 Gravitational wave astronomy
360(55)
12.1 Overview
360(2)
12.2 Astrophysical sources of gravitational waves
362(11)
12.3 Finding weak signals in noise: what is a detection?
373(23)
12.4 The first L1GO and Virgo detections
396(10)
12.5 Bibliography
406(9)
Exercises
407(8)
13 Cosmology
415(53)
13.1 What is cosmology?
415(3)
13.2 Cosmological kinematics: observing our expanding Universe
418(20)
13.3 Cosmological dynamics: understanding the expanding Universe
438(9)
13.4 Physical cosmology: the evolution of the Universe we observe
447(15)
13.5 Bibliography
462(6)
Exercises
463(5)
Appendix A Summary of linear algebra 468(4)
References 472(19)
Index 491
Bernard Schutz is a Professor in the School of Physics and Astronomy at Cardiff University, Wales, and Director (ret.) at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany. In 2019 he was elected a member of the US National Academy of Sciences, and in 2021, he was elected a fellow of the Royal Society, in recognition of his seminal contributions to relativistic astrophysics.