Relativity: Special, General, and Cosmological

by Wolfgang Rindler

Overview

This text is a considerable amplification and modernization of the authors' earlier Essential Relativity. It brings relativity alive conceptually and emphasizes the foundations and the logical subtleties rather than the mathematics or the detailed experiments. It includes 300 exercises and promotes a visceral understanding and the confidence to tackle any fundamental relativistic problem. Following a critical overview of the whole field, special-relativistic kinematics is presented three dimensionally before the mathematical level gradually rises. Four vectors preceded mechanics, four tensors precede Maxwell theory, and three chapters on cosmology end the text. This book brings the challenge and excitement of modern relativity and cosmology at a rigorous mathematical level within the reach of advanced undergraduates, while containing enough new material to interest lecturers and researchers.

Product Details

ISBN-13:	9780198508359
Publisher:	Oxford University Press
Publication date:	10/18/2001
Pages:	442
Product dimensions:	6.00(w) x 9.00(h) x 1.10(d)

About the Author

Professor Wolfgang Rindler
Department of Physics
The University of Texas at Dallas
Richardson, TX 75083-0688
USA

Table of Contents

	Introduction	1
1	From absolute space and time to influenceable spacetime: an overview	3
1.1	Definition of relativity	3
1.2	Newton's laws and intertial frames	4
1.3	The Galilean transformation	5
1.4	Newtonian relativity	6
1.5	Objections to absolute space; Mach's principle	7
1.6	The ether	9
1.7	Michelson and Morley's search for the ether	9
1.8	Lorentz's ether theory	10
1.9	Origins of special relativity	12
1.10	Further arguments for Einstein's two postulates	14
1.11	Cosmology and first doubts about inertial frames	15
1.12	Inertial and gravitational mass	16
1.13	Einstein's equivalence principle	18
1.14	Preview of general relativity	20
1.15	Caveats on the equivalence principle	22
1.16	Gravitational frequency shift and light bending	24
	Exercises 1	27
I	Special Relativity	31
2	Foundations of special relativity; The Lorentz transformation	33
2.1	On the nature of physical theories	33
2.2	Basic features of special relativity	34
2.3	Relativistic problem solving	36
2.4	Relativity of simultaneity, time-dilation and length-contraction: a preview	38
2.5	The relativity principle and the homogeneity and isotropy of inertial frames	39
2.6	The coordinate lattice; Definitions of simultaneity	41
2.7	Derivation of the Lorentz transformation	43
2.8	Properties of the Lorentz transformation	47
2.9	Graphical representation of the Lorentz transformation	49
2.10	The relativistic speed limit	54
2.11	Which transformations are allowed by the relativity principle?	57
	Exercises 2	58
3	Relativistic kinematics	61
3.1	Introduction	61
3.2	World-picture and world-map	61
3.3	Length contraction	62
3.4	Length contraction paradox	63
3.5	Time dilation; The twin paradox	64
3.6	Velocity transformation; Relative and mutual velocity	68
3.7	Acceleration transformation; Hyperbolic motion	70
3.8	Rigid motion and the uniformly accelerated rod	71
	Exercises 3	73
4	Relativistic optics	77
4.1	Introduction	77
4.2	The drag effect	77
4.3	The Doppler effect	78
4.4	Aberration	81
4.5	The visual appearance of moving objects	82
	Exercises 4	85
5	Spacetime and four-vectors	89
5.1	The discovery of Minkowski space	89
5.2	Three-dimensional Minkowski diagrams	90
5.3	Light cones and intervals	91
5.4	Three-vectors	94
5.5	Four-vectors	97
5.6	The geometry of four-vectors	101
5.7	Plane waves	103
	Exercises 5	105
6	Relativistic particle mechanics	108
6.1	Domain of sufficient validity of Newtonian mechanics	108
6.2	The axioms of the new mechanics	109
6.3	The equivalence of mass and energy	111
6.4	Four-momentum identities	114
6.5	Relativistic billiards	115
6.6	The zero-momentum frame	117
6.7	Threshold energies	118
6.8	Light quanta and de Broglie waves	119
6.9	The Compton effect	121
6.10	Four-force and three-force	123
	Exercises 6	126
7	Four-tensors; Electromagnetism in vacuum	130
7.1	Tensors: Preliminary ideas and notations	130
7.2	Tensors: Definition and properties	132
7.3	Maxwell's equations in tensor form	139
7.4	The four-potential	143
7.5	Transformation of e and b; The dual field	146
7.6	The field of a uniformly moving point charge	148
7.7	The field of an infinite straight current	150
7.8	The energy tensor of the electromagnetic field	151
7.9	From the mechanics of the field to the mechanics of material continua	154
	Exercises 7	157
II	General Relativity	163
8	Curved spaces and the basic ideas of general relativity	165
8.1	Curved surfaces	165
8.2	Curved spaces of higher dimensions	169
8.3	Riemannian spaces	172
8.4	A plan for general relativity	177
	Exercises 8	180
9	Static and stationary spacetimes	183
9.1	The coordinate lattice	183
9.2	Synchronization of clocks	184
9.3	First standard form of the metric	186
9.4	Newtonian support for the geodesic law of motion	188
9.5	Symmetries and the geometric characterization of static and stationary spacetimes	191
9.6	Canonical metric and relativistic potentials	195
9.7	The uniformly rotating lattice in Minkowski space	198
	Exercises 9	200
10	Geodesics, curvature tensor and vacuum field equations	203
10.1	Tensors for general relativity	203
10.2	Geodesics	204
10.3	Geodesic coordinates	208
10.4	Covariant and absolute differentiation	210
10.5	The Riemann curvature tensor	217
10.6	Einstein's vacuum field equations	221
	Exercises 10	224
11	The Schwarzschild metric	228
11.1	Derivation of the metric	228
11.2	Properties of the metric	230
11.3	The geometry of the Schwarzschild lattice	231
11.4	Contributions of the spatial curvature to post-Newtonian effects	233
11.5	Coordinates and measurements	235
11.6	The gravitational frequency shift	236
11.7	Isotropic metric and Shapiro time delay	237
11.8	Particle orbits in Schwarzschild space	238
11.9	The precession of Mercury's orbit	241
11.10	Photon orbits	245
11.11	Deflection of light by a spherical mass	248
11.12	Gravitational lenses	250
11.13	de Sitter precession via rotating coordinates	252
	Exercises 11	254
12	Black holes and Kruskal space	258
12.1	Schwarzschild black holes	258
12.2	Potential energy; A general-relativistic 'proof' of E = mc[superscript 2]	263
12.3	The extendibility of Schwarzschild spacetime	265
12.4	The uniformly accelerated lattice	267
12.5	Kruskal space	272
12.6	Black-hole thermodynamics and related topics	279
	Exercises 12	281
13	An exact plane gravitational wave	284
13.1	Introduction	284
13.2	The plane-wave metric	284
13.3	When wave meets dust	287
13.4	Inertial coordinates behind the wave	288
13.5	When wave meets light	290
13.6	The Penrose topology	291
13.7	Solving the field equation	293
	Exercises 13	295
14	The full field equations; de Sitter space	296
14.1	The laws of physics in curved spacetime	296
14.2	At last, the full field equations	299
14.3	The cosmological constant	303
14.4	Modified Schwarzschild space	304
14.5	de Sitter space	306
14.6	Anti-de Sitter space	312
	Exercises 14	314
15	Linearized general relativity	318
15.1	The basic equations	318
15.2	Gravitational waves. The TT gauge	323
15.3	Some physics of plane waves	325
15.4	Generation and detection of gravitational waves	330
15.5	The electromagnetic analogy in linearized GR	335
	Exercises 15	341
III	Cosmology	345
16	Cosmological spacetimes	347
16.1	The basic facts	347
16.2	Beginning to construct the model	358
16.3	Milne's model	360
16.4	The Friedman-Robertson-Walker metric	363
16.5	Robertson and Walker's theorem	368
	Exercises 16	369
17	Light propagation in FRW universes	373
17.1	Representation of FRW universes by subuniverses	373
17.2	The cosmological frequency shift	374
17.3	Cosmological horizons	376
17.4	The apparent horizon	382
17.5	Observables	384
	Exercises 17	388
18	Dynamics of FRW universes	391
18.1	Applying the field equations	391
18.2	What the field equations tell us	393
18.3	The Friedman models	396
18.4	Once again, comparison with observation	405
18.5	Inflation	409
18.6	The anthropic principle	413
	Exercises 18	415
Appendix	Curvature tensor components for the diagonal metric	417
	Index	421

Editorial Reviews

"A textbook for graduate or advanced undergraduate physics students who are familiar with calculus up to partial differentiation, ordinary vector, and the binomial theorem. Rindler (physics, U. of Texas-Dallas) has essentially rewritten his earlier Essential Relativity to account for the growing sophistication and inquisitiveness about relativity in mainstream physics. He does not provide a bibliography."—SciTech Book News

"This book should be on the shelf of all who are intrigued by the startling modern advances in our understanding of space and time."—American Journal of Physics

From the Publisher