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Relativity Made Relatively Easy Volume 2: General Relativity and Cosmology [Pehme köide]

(Professor of Physics, Department of Physics, University of Oxford)
  • Formaat: Paperback / softback, 512 pages, kõrgus x laius x paksus: 247x190x24 mm, kaal: 1072 g, 17 halftones, 89 line art illustrations, 3 combo illustrations
  • Ilmumisaeg: 02-Nov-2021
  • Kirjastus: Oxford University Press
  • ISBN-10: 0192893548
  • ISBN-13: 9780192893543
Teised raamatud teemal:
  • Formaat: Paperback / softback, 512 pages, kõrgus x laius x paksus: 247x190x24 mm, kaal: 1072 g, 17 halftones, 89 line art illustrations, 3 combo illustrations
  • Ilmumisaeg: 02-Nov-2021
  • Kirjastus: Oxford University Press
  • ISBN-10: 0192893548
  • ISBN-13: 9780192893543
Teised raamatud teemal:
Following on from a previous volume on Special Relativity, Andrew Steane's second volume on General Relativity and Cosmology is aimed at advanced undergraduate or graduate students undertaking a physics course, and encourages them to expand their knowledge of Special Relativity.

Beginning with a survey of the main ideas, the textbook goes on to give the methodological foundations to enable a working understanding of astronomy and gravitational waves (linearized approximation, differential geometry, covariant differentiation, physics in curved spacetime). It covers the
generic properties of horizons and black holes, including Hawking radiation, introduces the key concepts in cosmology and gives a grounding in classical field theory, including spinors and the Dirac equation, and a Lagrangian approach to General Relativity.

The textbook is designed for self-study and is aimed throughout at clarity, physical insight, and simplicity, presenting explanations and derivations in full, and providing many explicit examples.

Arvustused

Review from previous edition As Albert Einstein once emphasized, one should make things as simple as possible, but not simpler. Andrew Steane follows the master's recommendation and presents a relatively easy tour through the wonderful worlds of Special and General Relativity. He guides the reader patiently and pedagogically through the fundamental concepts as well as their main applications. This book is of great value for both students and lecturers. * Claus Kiefer, Institute for Theoretical Physics, University of Cologne * Steane's book provides a physically oriented introduction to Special Relativity and its consequences, which does not compromise rigour in its exposition. I do not know of any other textbook on the topic covering such a breadth of topics at a detailed, but at the same time accessible and insightful level. In particular, the discussion of electromagnetism in the context of Special Relativity - where Relativity really comes into life - is excellent. The book contains an interesting and original selection of exercises which will help the dedicated reader to gain mastery in the details of the theory. * Juan A. Valiente Kroon, School of Mathematical Sciences, Queen Mary, University of London * Offering a uniquely broad and thorough coverage of one of the standard tools of modern physics, Andrew Steane's Relativity Made Relatively Easy is an approachable and comprehensive coverage of Einstein's most famous contribution to science. It is sure to become a favorite resource for students and researchers alike. * Warren Anderson, Center for Gravitation and Cosmology, University of Wisconsin-Milwaukee * The book truly has the potential to become a pivotal part of scholarship in physics. This lucid and thoughtful approach to taking the reader pedagogically through how Einsteinian relativity works, and how it supersedes the Newtonian construction with respect to explaining the basic principles of physical law, is comprehensive, thorough, innovative, challenging, and in many cases original. Steane's approach fills a gap in what in many university undergraduate courses has become a topic considered rather too briefly and in a rather too stereotyped manner, and which thereby has always denied physics graduates of the deeper insight into how Lorentz invariance is at the root of almost everything. * John Dainton, Sir James Chadwick Professor of Physics, University of Liverpool *

Preface v
Acknowledgements vii
1 Terminology and notation
1(10)
Exercises
7(4)
Part I
2 The elements of General Relativity
11(16)
2.1 The gravitational field equations: first view
12(7)
2.2 The strong equivalence principle
19(5)
2.3 The source of gravity
24(2)
Exercises
26(1)
3 An introductory example: the uniform static field
27(5)
Exercises
31(1)
4 Life in a rotating world
32(8)
4.1 The canonical form of the stationary metric
37(1)
4.2 The lessons of the rotating cylinder
38(1)
Exercises
39(1)
5 Linearized General Relativity
40(16)
5.1 Global Lorentz transformations
42(2)
5.2 Coordinate transformations and gauge transformations
44(1)
5.3 The linearized field equations
45(4)
5.4 Newtonian limit
49(2)
5.5 Field energy and the gravity of gravity
51(3)
Exercises
54(2)
6 Slow stationary sources
56(9)
6.1 Gravitational 'Maxwell's equations'
56(3)
6.2 Lense-Thirring precession
59(3)
Exercises
62(3)
7 Gravitational waves
65(30)
7.1 Identifying and simplifying the plane wave solutions
65(2)
7.2 The physical impact of a gravitational wave
67(6)
7.3 Sources of gravitational waves
73(5)
7.4 Energy flux in gravitational waves
78(6)
7.5 The detection of gravitational radiation
84(6)
Exercises
90(5)
Part II
8 Manifolds
95(14)
8.1 The manifold
95(4)
8.2 Riemannian manifolds
99(4)
8.3 Local flatness and Riemann normal coordinates
103(3)
8.4 Measuring length, area and volume
106(2)
Exercises
108(1)
9 Vectors on manifolds
109(12)
9.1 Basis vectors and the inner product
110(8)
9.2 An example: plane polar coordinates
118(2)
Exercises
120(1)
10 The affine connection
121(12)
10.1 Connection coefficients and covariant derivative
121(7)
10.2 Differentiation along a curve
128(2)
10.3 Extending the example: plane polar coordinates
130(1)
Exercises
131(2)
11 Further useful ideas
133(11)
11.1 Some physics related to 4-velocity
133(2)
11.2 Tetrads
135(2)
11.3 Vector operators
137(3)
11.4 Gauss' divergence theorem
140(2)
Exercises
142(2)
12 Tensors
144(16)
12.1 The components of a tensor
145(3)
12.2 Transformation of Γ and relation to geodesic coordinates
148(2)
12.3 Tensor algebra
150(1)
12.4 Covariant derivative of tensors
150(6)
12.5 Tensors of rank zero
156(1)
12.6 Tensor density and the Hodge dual
157(1)
Exercises
158(2)
13 Parallel transport and geodesics
160(18)
13.1 Parallel transport
160(6)
13.2 Metric geodesic: most proper time and least distance
166(2)
13.3 Inertial motion
168(1)
13.4 Conservation laws and Killing vectors
169(1)
13.5 Fermi-Walker transport
170(2)
13.6 Gravitational redshift
172(3)
13.7 Cause and effect
175(2)
Exercises
177(1)
14 Physics in curved spacetime
178(11)
14.1 Electromagnetism
179(2)
14.2 Fluid flow and continuous media
181(4)
14.3 How General Relativity works
185(2)
14.4 Generally covariant physics
187(1)
Exercises
188(1)
15 Curvature
189(24)
15.1 Quantifying curvature
189(6)
15.2 Relating Rabcd to parallel transport
195(5)
15.3 Geodesic deviation
200(5)
15.4 Lie derivative
205(2)
15.5 Symmetries of spacetime
207(4)
Exercises
211(2)
16 The Einstein field equation
213(16)
16.1 Derivation of the field equation
213(3)
16.2 Stability and energy conditions
216(1)
16.3 Field equation for a small region
217(3)
16.4 Motion of matter from the field equation
220(1)
16.5 The cosmological constant
221(1)
16.6 Energy and momentum
222(2)
Exercises
224(5)
Part III
17 Schwarzschild-Droste solution
229(20)
17.1 Obtaining the metric
229(4)
17.2 Orbits
233(8)
17.3 Light in Schwarzschild spacetime
241(5)
17.4 Tidal stress tensor
246(1)
Exercises
247(2)
18 Further spherically symmetric solutions
249(11)
18.1 Interior Schwarzschild solution
250(5)
18.2 Reissner-Nordstrom metric
255(3)
18.3 de Sitter-Schwarzschild metric
258(1)
Exercises
258(2)
19 Rotating bodies; the Kerr metric
260(14)
19.1 The general stationary axisymmetric metric
260(2)
19.2 Stationary limit surface and ergoregion
262(2)
19.3 The Kerr metric
264(4)
19.4 Freefall motion in the plane 0 = π/2
268(4)
Exercises
272(2)
20 Black holes
274(27)
20.1 Birkhoff's theorem
274(5)
20.2 Null surfaces and event horizons
279(4)
20.3 The Schwarzschild horizon
283(2)
20.4 Black hole formation
285(6)
20.5 Kruskal-Szekeres spacetime
291(5)
20.6 Astronomical evidence for black holes
296(3)
Exercises
299(2)
21 Black hole thermodynamics
301(18)
21.1 The Penrose process
301(3)
21.2 Area theorem and entropy
304(2)
21.3 Unruh and Hawking effects
306(7)
21.4 Laws of black hole mechanics
313(3)
Exercises
316(3)
Part IV
22 Cosmology
319(34)
22.1 Observed properties of the universe
319(11)
22.2 Cosmic time and space
330(4)
22.3 Friedmann-Lemaitre-Robertson-Walker metric
334(3)
22.4 Redshift in an expanding space
337(3)
22.5 Visualizing the evolution of a curved space
340(7)
22.6 Luminosity distance, angular diameter distance
347(2)
22.7 The cosmic distance ladder
349(3)
Exercises
352(1)
23 Cosmological dynamics
353(26)
23.1 The Friedmann equations
353(4)
23.2 Solving the Friedmann equations
357(12)
23.3 The physical interpretation of the cosmological constant
369(1)
23.4 Particle horizon and event horizon
370(5)
23.5 Last scattering
375(1)
Exercises
376(3)
24 The growth of structure
379(19)
24.1 The structure equations
381(3)
24.2 Linearized treatment
384(6)
24.3 The overall picture
390(4)
24.4 Baryon acoustic oscillations
394(1)
24.5 Galaxy formation
395(1)
Exercises
396(2)
25 Observational cosmology
398(19)
25.1 Models, statistical and systematic error
398(2)
25.2 The age of the universe
400(1)
25.3 Hubble parameter and deceleration parameter
401(5)
25.4 Baryon acoustic oscillations
406(3)
25.5 The cosmic microwave background radiation
409(7)
Exercises
416(1)
26 The very early universe
417(18)
26.1 The horizon and flatness 'problems'
419(3)
26.2 Inflation
422(10)
Exercises
432(3)
Part V
27 First steps in classical field theory
435(14)
27.1 Wave equation and Klein-Gordon equation
436(3)
27.2 The Dirac equation
439(3)
27.3 Lorentz transformation of spinors
442(7)
28 Lagrangian mechanics for fields
449(11)
28.1 Field energy
452(1)
28.2 Conserved quantities and Noether's theorem
453(3)
28.3 Interactions
456(1)
28.4 The Einstein-Hilbert action
457(3)
29 Conclusion
460(3)
Appendix A Kepler orbits for binary system 463(3)
Appendix B The 2-sphere and the 3-sphere 466(5)
B.1 The 2-sphere
466(2)
B.2 The 3-sphere
468(2)
B.3 Hyperbolic space
470(1)
Appendix C Differential operators as vectors 471(3)
Appendix D General equations of the linearized theory 474(4)
Appendix E Gravitational energy 478(3)
Appendix F Causality and the Cauchy problem in General Relativity 481(4)
References 485(4)
Index 489
Andrew Steane is a Professor of Physics at the University of Oxford. He has conducted experimental and theoretical research into the foundations of physics and has performed pioneering quantum experiments with ultra-cold atomic clouds, as well as establishing the ion trap quantum computing program at Oxford. Professor Steane discovered quantum error correction and the CSS (Calderbank Shor Steane) codes and he is a recipient of the Maxwell Medal and Prize of the Institute of Physics, and the Trotter Prize of Texas A&M University. He regularly lectures on relativity and other areas of physics and has published two undergraduate physics textbooks and two books on science and religion with Oxford University Press.