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Introducing Einstein's Relativity: A Deeper Understanding 2nd Revised edition [Pehme köide]

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(Emeritus Professor, University of Southampton), (Emeritus Professor, University of Southampton)
  • Formaat: Paperback / softback, 624 pages, kõrgus x laius x paksus: 245x190x28 mm, kaal: 1313 g, 240
  • Ilmumisaeg: 07-Jun-2022
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198862032
  • ISBN-13: 9780198862031
Teised raamatud teemal:
Introducing Einstein's Relativity: A Deeper Understanding 2nd Revised editionSuurem pilt
  • Formaat: Paperback / softback, 624 pages, kõrgus x laius x paksus: 245x190x28 mm, kaal: 1313 g, 240
  • Ilmumisaeg: 07-Jun-2022
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198862032
  • ISBN-13: 9780198862031
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780198862031.html
Märksõnad:
There is little doubt that Einstein's theory of relativity captures the imagination. Not only has it radically altered the way we view the universe, but the theory also has a considerable number of surprises in store. This is especially so in the three main topics of current interest that this book reaches, namely: black holes, gravitational waves, and cosmology.

The main aim of this textbook is to provide students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject. Indeed, the book follows Einstein in that it introduces the theory very much from a physical point of view. After introducing the special theory of relativity, the basic field equations of gravitation are derived and discussed carefully as a prelude to first solving them in simple cases and then exploring the three main areas of application.



This new edition contains a substantial extension content that considers new and updated developments in the field. Topics include coverage of the advancement of observational cosmology, the detection of gravitational waves from colliding black holes and neutron stars, and advancements in modern cosmology.

Einstein's theory of relativity is undoubtedly one of the greatest achievements of the human mind. Yet, in this book, the author makes it possible for students with a wide range of abilities to deal confidently with the subject. Based on both authors' experience teaching the subject this is achieved by breaking down the main arguments into a series of simple logical steps. Full details are provided in the text and the numerous exercises while additional insight is provided through the numerous diagrams. As a result this book makes an excellent course for any reader coming to the subject for the first time while providing a thorough understanding for any student wanting to go on to study the subject in depth
1 The organization of the book
1(12)
1.1 The evolution of the book
1(1)
1.2 Acknowledgements
2(1)
1.3 The status of scientific research
3(2)
1.4 A note for students on studying from a book
5(1)
1.5 A final note for the less able student from Ray
6(1)
1.6 A final note for the more able student from James
7(2)
1.7 Research interests of the authors
9(4)
Exercises
9(1)
Further reading
10(3)
Part A Special Relativity
2 The k-calculus
13(18)
2.1 Model building
13(1)
2.2 Historical background
14(1)
2.3 Newtonian framework
15(1)
2.4 Galilean transformations
16(1)
2.5 The principle of special relativity
17(1)
2.6 The constancy of the velocity of light
18(1)
2.7 The k-factor
19(1)
2.8 Relative speed of two inertial observers
20(1)
2.9 Composition law for velocities
21(1)
2.10 The relativity of simultaneity
22(1)
2.11 Causality
23(1)
2.12 The clock paradox
24(1)
2.13 The Lorentz transformations
25(1)
2.14 The four-dimensional world view
26(5)
Exercises
28(1)
Further reading
29(2)
3 The key attributes of special relativity
31(18)
3.1 Standard derivation of the Lorentz transformations
31(2)
3.2 Mathematical properties of Lorentz transformations
33(2)
3.3 Length contraction
35(1)
3.4 Time dilation
36(1)
3.5 Transformation of velocities
37(1)
3.6 Relationship between space-time diagrams of inertial observers
38(2)
3.7 Acceleration in special relativity
40(1)
3.8 Uniform acceleration
40(2)
3.9 The twin paradox
42(1)
3.10 The Doppler effect
43(6)
Exercises
45(2)
Further reading
47(2)
4 The elements of relativistic mechanics
49(16)
4.1 Newtonian theory
49(2)
4.2 Isolated systems of particles in Newtonian mechanics
51(1)
4.3 Relativistic mass
52(2)
4.4 Relativistic energy
54(3)
4.5 Photons
57(8)
Exercises
59(2)
Further reading
61(4)
Part B The Formalism of Tensors
5 Tensor algebra
65(20)
5.1 Introduction
65(1)
5.2 Manifolds and coordinates
66(1)
5.3 Curves and surfaces
67(1)
5.4 Transformation of coordinates
68(3)
5.5 Contravariant tensors
71(1)
5.6 Covariant tensors
72(2)
5.7 Mixed tensors
74(1)
5.8 Tensor fields
75(1)
5.9 Elementary operations with tensors
75(3)
5.10 Index-free interpretation of contravariant vector fields
78(7)
Exercises
81(2)
Further reading
83(2)
6 Tensor calculus
85(30)
6.1 Partial derivative of a tensor
85(1)
6.2 The Lie derivative
86(4)
6.3 The affine connection and covariant differentiation
90(2)
6.4 Affine geodesies
92(2)
6.5 The Riemann tensor
94(1)
6.6 Geodesic coordinates
95(1)
6.7 Affine flatness
96(4)
6.8 The metric
100(1)
6.9 Metric geodesies
101(2)
6.10 The metric connection
103(1)
6.11 Metric flatness
104(1)
6.12 The curvature tensor
105(2)
6.13 The Weyl tensor
107(8)
Exercises
108(4)
Further reading
112(3)
7 Integration, variation, and symmetry
115(20)
7.1 Tensor densities
115(1)
7.2 The Levi-Civita alternating symbol
116(1)
7.3 The metric determinant
117(3)
7.4 Integrals and Stokes' theorem
120(2)
7.5 The Euler-Lagrange equations
122(3)
7.6 The variational method for geodesies
125(3)
7.7 Isometries
128(7)
Exercises
130(2)
Further reading
132(3)
Part C General Relativity
8 Special relativity revisited
135(18)
8.1 Minkowski space-time
135(2)
8.2 The null cone
137(1)
8.3 The Lorentz group
138(2)
8.4 Proper time
140(2)
8.5 An axiomatic formulation of special relativity
142(2)
8.6 A variational principle approach to classical mechanics
144(2)
8.7 A variational principle approach to relativistic mechanics
146(2)
8.8 Covariant formulation of relativistic mechanics
148(5)
Exercises
149(2)
Further reading
151(2)
9 The principles of general relativity
153(18)
9.1 The role of physical principles
153(1)
9.2 Mach's principle
154(5)
9.3 Mass in Newtonian theory
159(3)
9.4 The principle of equivalence
162(3)
9.5 The principle of general covariance
165(1)
9.6 The principle of minimal gravitational coupling
165(1)
9.7 The correspondence principle
166(5)
Exercises
167(1)
Further reading
168(3)
10 The field equations of general relativity
171(16)
10.1 Non-local lift experiments
171(1)
10.2 The Newtonian equation of deviation
172(1)
10.3 The equation of geodesic deviation
173(2)
10.4 The vacuum field equations of general relativity
175(1)
10.5 Freely falling frames
176(2)
10.6 The Newtonian correspondence
178(4)
10.7 Einstein's route to the field equations of general relativity
182(2)
10.8 The full field equations of general relativity
184(3)
Exercises
185(1)
Further reading
186(1)
11 General relativity from a variational principle
187(1)
11.1 The Palatini equation
187(1)
11.2 Differential constraints on the field equations
188(1)
11.3 A simple example
189(1)
11.4 The Einstein Lagrangian
190(2)
11.5 Indirect derivation of the field equations
192(1)
11.6 An equivalent Lagrangian
193(2)
11.7 The Palatini approach
195(2)
11.8 The full field equations
197(1)
Exercises
198(3)
Further reading
201(2)
12 The energy-momentum tensor
203(1)
12.1 Preview
203(1)
12.2 Incoherent matter
203(3)
12.3 The coupling constant
206(1)
12.4 Perfect fluid
207(1)
12.5 Maxwell's equations
208(2)
12.6 Potential formulation of Maxwell's equations
210(1)
12.7 The Maxwell energy-momentum tensor
211(2)
12.8 Other energy-momentum tensors
213(1)
12.9 The dominant energy condition
214(3)
Exercises
215(1)
Further reading
216(1)
13 The structure of the field equations
217(19)
13.1 Interpretation of the field equations
217(1)
13.2 Determinacy, non-linearity, and differentiability
218(2)
13.3 The cosmological term
220(2)
13.4 The conservation equations
222(1)
13.5 The Cauchy problem
223(3)
13.6 Einstein's equations as evolution equations
226(3)
13.7 Solving Einstein's equations in harmonic coordinates
229(2)
13.8 The hole problem
231(1)
13.9 The equivalence problem
232(1)
13.10 The status of exact solutions
232(4)
Exercises
235(1)
1 Further reading
236(3)
14 The 3+1 and 2+2 formalisms
239(30)
14.1 The geometry of submanifolds
239(1)
14.2 The induced metric
240(1)
14.3 The induced covariant derivative
241(2)
14.4 The Gauss-Codazzi equations
243(2)
14.5 Calculating the Gauss equation
245(1)
14.6 Calculating the Codazzi equation
246(1)
14.7 The geometry of foliations
247(1)
14.8 Derivation of the Ricci equation
248(1)
14.9 The lapse function
249(3)
14.10 The 3+1 decomposition of the metric
252(1)
14.11 The 3+1 decomposition of the vacuum Einstein equations
253(4)
14.12 The 3+1 equations and numerical relativity
257(4)
14.13 The 2+2 and characteristic approaches
261(2)
14.14 The 2+2 metric decomposition
263(6)
Exercises
266(2)
Further reading
268(1)
15 The Schwarzschild solution
269(20)
15.1 Stationary solutions
269(1)
15.2 Hypersurface-orthogonal vector fields
270(2)
15.3 Static solutions
272(2)
15.4 Spherically symmetric solutions
274(3)
15.5 The Schwarzschild solution
277(2)
15.6 Properties of the Schwarzschild solution
279(2)
15.7 Isotropic coordinates
281(1)
15.8 The Schwarzschild interior solution
282(7)
Exercises
284(3)
Further reading
287(2)
16 Classical experimental tests of general relativity
289(32)
16.1 Introduction
289(1)
16.2 Gravitational red shift
290(3)
16.3 The Eotvtis experiment
293(1)
16.4 The Einstein equivalence principle
294(2)
16.5 Classical Kepler motion
296(2)
16.6 Advance of the perihelion of Mercury
298(5)
16.7 Bending of light
303(4)
16.8 Time delay of light
307(2)
16.9 The PPN parameters
309(3)
16.10 A chronology of experimental and observational events
312(1)
16.11 Rubber-sheet geometry
313(8)
Exercises
315(3)
Further reading
318(3)
Part D Black Holes
17 Non-rotating black holes
321(22)
17.1 Characterization of coordinates
321(2)
17.2 Singularities
323(1)
17.3 Spatial and space-time diagrams
324(1)
17.4 Space-time diagram in Schwarzschild coordinates
325(2)
17.5 A radially infalling particle
327(1)
17.6 Eddington-Finkelstein coordinates
328(3)
17.7 Event horizons
331(1)
17.8 Black holes
332(2)
17.9 A Newtonian argument
334(1)
17.10 Tidal forces in a black hole
335(2)
17.11 Observational evidence for black holes
337(1)
17.12 Theoretical status of black holes
338(5)
Exercises
340(2)
Further reading
342(1)
18 Maximal extension and conformal compaerification
343(12)
18.1 Maximal analytic extensions
343(1)
18.2 The Kruskal solution
343(3)
18.3 The Einstein-Rosen bridge
346(1)
18.4 Penrose diagram for Minkowski space-time
347(4)
18.5 Penrose diagram for the Kruskal solution
351(4)
Exercises
352(1)
Further reading
353(2)
19 Charged black holes
355(12)
19.1 The field of a charged mass point
355(2)
19.2 Intrinsic and coordinate singularities
357(1)
19.3 Space-time diagram of the Reissner-Nordstrom solution
358(2)
19.4 Neutral particles in Reissner-Nordstrom space-time
360(1)
19.5 Penrose diagrams of the maximal analytic extensions
361(6)
Exercises
364(2)
Further reading
366(1)
20 Rotating black holes
367(34)
20.1 Null tetrads
367(2)
20.2 The Kerr solution from a complex transformation
369(1)
20.3 The three main forms of the Kerr solution
370(2)
20.4 Basic properties of the Kerr solution
372(2)
20.5 Singularities and horizons
374(3)
20.6 The principal null congruences
377(2)
20.7 Eddington-Finkelstein coordinates
379(2)
20.8 The stationary limit
381(1)
20.9 Maximal extension for the case a2 < m2
382(2)
20.10 Maximal extension for the case a > m
384(1)
20.11 Rotating black holes
385(3)
20.12 The definition of mass in general relativity
388(3)
20.13 The singularity theorems
391(3)
20.14 Black hole thermodynamics and Hawking radiation
394(7)
Exercises
396(1)
Further reading
397(4)
Part E Gravitational Waves
21 Linearized gravitational waves and their detection
401(50)
21.1 The linearized field equations
401(2)
21.2 Gauge transformations
403(2)
21.3 Linearized plane gravitational waves
405(4)
21.4 Polarization states of plane waves
409(2)
21.5 Solving the wave equation
411(5)
21.6 The quadrupole formula
416(1)
21.7 The quadrupole generated by a binary star system
417(3)
21.8 Gravitational energy
420(4)
21.9 Gravitational energy-flux from a binary system
424(3)
21.10 Effects of gravitational radiation on the orbit of a binary system
427(3)
21.11 Measuring gravitational wave displacements
430(5)
21.12 A direct interferometric measurement
435(2)
21.13 The detection of gravitational waves
437(3)
21.14 Sources of gravitational radiation and the observation of gravitational waves
440(11)
Exercises
444(5)
Further reading
449(2)
22 Exact gravitational waves
451(10)
22.1 Gravitational waves and symmetries
451(1)
22.2 Einstein-Rosen waves
451(3)
22.3 Exact plane wave solutions
454(1)
22.4 Impulsive plane gravitational waves
455(2)
22.5 Colliding impulsive plane gravitational waves
457(1)
22.6 Colliding gravitational waves
458(3)
Exercises
459(1)
Further reading
460(1)
23 Radiation from an isolated source
461(20)
23.1 Radiating isolated sources
461(1)
23.2 Characteristic hypersurfaces of Einstein's equations
462(1)
23.3 Radiation coordinates
463(2)
23.4 Bondi's radiating metric
465(2)
23.5 The characteristic initial value problem
467(1)
23.6 News and mass loss
468(3)
23.7 The Petrov classification
471(2)
23.8 The peeling theorem
473(1)
23.9 The optical scalars
474(7)
Exercises
476(2)
Further reading
478(3)
Part F Cosmology
24 Relativistic cosmology
481(30)
24.1 Preview
481(2)
24.2 Olbers' paradox
483(1)
24.3 Newtonian cosmology
484(3)
24.4 The cosmological principle
487(2)
24.5 Weyl's postulate
489(1)
24.6 Standard models of relativistic cosmology
490(2)
24.7 Spaces of constant curvature
492(3)
24.8 The geometry of 3-spaces of constant curvature
495(4)
24.9 Friedmann's equation
499(3)
24.10 Propagation of light
502(2)
24.11 A cosmological definition of distance
504(1)
24.12 Hubble's law in relativistic cosmology
505(6)
Exercises
508(2)
Further reading
510(1)
25 The classical cosmological models
511(28)
25.1 The flat space models
511(3)
25.2 Models with vanishing cosmological constant
514(2)
25.3 Classification of Friedmann models
516(3)
25.4 The Einstein static model and the de Sitter model
519(2)
25.5 Early epochs of the universe
521(1)
25.6 The steady-state theory
522(1)
25.7 The event horizon of the de Sitter universe
523(3)
25.8 Particle and event horizons
526(1)
25.9 Lorentzian constant curvature space-times
527(3)
25.10 Conformal structure of Robertson-Walker space-times
530(1)
25.11 Conformal structure of de Sitter and anti-de Sitter space-time
531(3)
25.12 Our model of the universe
534(5)
Exercises
535(2)
Further reading
537(2)
26 Modern cosmology
539(56)
26.1 Multi-component models
539(6)
26.2 Measuring the Hubble constant
545(2)
26.3 The cosmic microwave background radiation
547(4)
26.4 How heavy is the universe?
551(4)
26.5 The ACDM model of cosmology
555(3)
26.6 The early Universe
558(2)
26.7 Inflationary cosmology
560(5)
26.8 The anthropic principle
565(2)
26.9 Final questions
567(28)
Exercises
569(2)
Further reading
571(2)
Answers to exercises
573(22)
Selected bibliography 595(4)
Index 599
Professor Ray d'Inverno is Emeritus Professor in General Relativity at the University of Southhampton. A pioneer in the use of computer algebra in general relativity, Professor d'Inverno developed the early system LAM (Lisp Algebraic Manipulator), which was a precursor to Sheep, the system most used to date in the study of exact solutions and their invariant classification. He also developed the 2+2 formalism for analysing the initial value problem in general relativity. The formalism has also been used to provide a possible route towards a canonical quantization programme for the theory. In addition, he worked in numerical relativity (solving Einstein's equations numerically on a computer) and with others set up the CCM (Cauchy-Characteristic Matching) approach, which is still used in this increasingly important field.



James Vickers is an Emeritus Professor of Mathematics at the University of Southampton and has published extensively on general relativity. His early research was on the structure of weak singularities in relativity and more recently he has given proofs of both the Penrose and Hawking singularity theorems for low-regularity spacetimes. These show that the singularities predicted by these theorems must be accompanied by unbounded curvature. He has also worked on the asymptotic structure of space-time and used spinors to prove the positivity of the Bondi mass.