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Gravity, Black Holes, and the Very Early Universe : An Introduction to General Relativity and Cosmology - Tai L. Chow

Gravity, Black Holes, and the Very Early Universe

An Introduction to General Relativity and Cosmology


Published: 1st November 2007
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Chow introduces the mathematical methods essential to understanding and applying general relativity--tensor calculus, some differential geometry, etc.--but leaves to more advanced references derivations that a beginning student would likely find overly long and tedious. The book employs standard tensor analysis--which requires only basic calculus for its understanding--and resists the temptation to adopt more powerful mathematical formalisms (like exterior calculus and differential forms) used by researchers in the field. In this way, the student can concentrate on learning physics--and not be distracted by the complexities of unfamiliar mathematical methods.

The book also offers comprehensive discussion of the physics of black holes. The author hits just the right level of presentation: sufficient mathematical detail to demonstrate or make plausible the physical attributes of black holes - in contrast to "hand-waving" discussions found in popularizations of the subject - yet not so much mathematics as to lose track of the physics in an impenetrable forest of equations. An equally strong point is the author's discussion of the most exciting contemporary issues in astrophysics apart from black holes: recent measurements of the cosmic microwave background, the existence of the cosmological constant, dark matter, dark energy and the accelerated expansion of the universe. The final chapters on unification and inflation are also very well done and not generally found in other introductory treatments of general relativity.

In sum, the book is highly informative and has a user-friendly style, which should make it an attractive choice for teachers and students.

From the reviews:

"Chow ... has successfully filled the gap in the literature between introductory texts for lay readers interested in cosmology and advanced works. Chow's book is aimed at undergraduates but is accessible to all readers ... . Chapters can stand alone for quick reference, yet the book's progressive nature makes it a viable course resource for supporting all physics curricula. ... this work will be suitable for all science libraries and collections. Summing Up: Recommended. General readers; lower-division undergraduates through graduate students." (J. H. Murphy, CHOICE, Vol. 45 (8), 2008)

"This book has its roots in the lecture notes of Professor Chow, who taught an undergraduate course in relativity and cosmology ... . I was interested by the ideas and the historical aspects developed ... on the inflationary universe and the physics of the very early universe. ... The book may be useful for general information on cosmology and to a physicist already well prepared in general relativity and cosmology to prepare a course on these subjects." (Fernande Grandjean, Belgian Physical Society Magazine, Issue 2, June, 2009)

About the Authorp. vii
Prefacep. ix
Basic Ideas of General Relativityp. 1
Inadequacy of Special Relativityp. 1
Einstein's Principle of Equivalencep. 3
Immediate Consequences of the Principle of Equivalencep. 7
The Bending of a Light Beamp. 7
Gravitational Shift of Spectral Lines (Gravitational Redshift)p. 8
The Curved Space-Time Conceptp. 8
The Principle of General Covariancep. 12
Distance and Time Intervalsp. 13
Problemsp. 15
Referencesp. 17
Curvilinear Coordinates and General Tensorsp. 19
Curvilinear Coordinatesp. 19
Parallel Displacement and Covariant Differentiationp. 23
Symmetry Properties of the Christoffel Symbolsp. 27
Christoffel Symbols and the Metric Tensorp. 28
Geodesicsp. 29
The Stationary Property of Geodesicsp. 30
The Curvature Tensorp. 32
The Condition for Flat Spacep. 36
Geodesic Deviationp. 37
Laws of Physics in Curved Spacesp. 38
The Metric Tensor and the Classical Gravitational Potentialp. 39
Some Useful Calculation Toolsp. 40
Problemsp. 43
Referencesp. 44
Einstein's Law of Gravitationp. 45
Introduction (Summary of General Principles)p. 45
A Heuristic Derivation of Einstein's Equationsp. 46
Vacuum Field Equationsp. 46
Field Equations Where Matter is Present in Spacep. 48
Energy-Momentum Tensorp. 51
Gravitational Radiationp. 52
Problemsp. 54
Referencesp. 54
The Schwarzschild Solutionp. 55
The Schwarzschild Metricp. 55
The Schwarzschild Solution of the Vacuum Field Equationsp. 56
Schwarzschild Geodesicsp. 60
Quasiuniform Gravitational Fieldp. 62
Problemsp. 63
Referencesp. 63
Experimental Tests of Einstein's Theoryp. 65
Precession of the Perihelion of Mercuryp. 65
Deflection of Light Rays in a Gravitational Fieldp. 71
Light Retardation (The Shapiro Experiment)p. 75
Test of Gravitational Radiation (Hulse-Taylor's Measurement of the Orbital Decay of the Binary Pulsar PSR-1913+16)p. 77
Problemsp. 79
Referencesp. 79
The Physics of Black Holesp. 81
The Schwarzschild Black Holep. 81
Inside a Black Holep. 84
How a Black Hole May Formp. 86
The Kerr-Newman Black Holep. 89
Energy Extraction from a Rotating Black Hole: The Penrose Processp. 92
The Area Theoremp. 93
Energy Extraction from Two Coalescing Black Holesp. 94
Thermodynamics of Black Holesp. 95
Quantum Mechanics of Black Holes: Hawking Radiationp. 97
The Detection of Black Holesp. 101
Detection of Stellar-Mass Black Holesp. 101
Supermassive Black Holes in the Centers of Galaxiesp. 104
Intermediate-Mass Black Holesp. 106
How Do Electrical and Gravitational Fields Get Out of Black Holes?p. 106
Black Holes and Particle Physicsp. 107
Problemsp. 108
Referencesp. 109
Introduction to Cosmologyp. 111
Introductionp. 111
The Development of Western Cosmological Conceptsp. 112
Ancient Greecep. 112
The Renaissance of Cosmologyp. 113
Newton and the Infinite Universep. 114
Newton's Law of Gravity and a Nonstationary Universep. 115
Olbers' Paradoxp. 118
The Discovery of the Expansion of the Universep. 119
The Big Bangp. 123
The Microwave Background Radiationp. 124
Additional Evidence for the Big Bangp. 128
Problemsp. 130
Referencesp. 131
Big Bang Modelsp. 133
The Cosmic Fluid and Fundamental Observersp. 133
Properties of the Robertson-Walker Metricp. 135
Cosmic Dynamics and Friedmann's Equationsp. 139
The Solutions of Friedmann's Equationsp. 142
Flat Model (k = 0)p. 143
Closed Model (k = 1)p. 144
Open Model (k = -1)p. 146
Dark Matter and the Fate of the Universep. 148
The Beginning, the End, and Time's Arrowp. 152
An Accelerating Universe?p. 156
The Cosmological Constantp. 158
Problemsp. 161
Referencesp. 161
Particles, Forces, and Unification of Forcesp. 163
Particlesp. 163
Spinp. 163
Fermionsp. 164
Bosonsp. 165
Hadrons and Leptonsp. 165
Quarksp. 167
Quark Colorsp. 168
Quark Confinementp. 169
Fundamental Interactions and Conservation Lawsp. 171
Spontaneous Symmetry Breakingp. 177
Unification of Forces (Interactions)p. 180
The Negative Vacuum Pressurep. 184
Referencesp. 186
The Inflationary Universep. 187
The Flatness Problemp. 187
The Horizon Problemp. 188
Alan Guth's Inflationary Theoryp. 191
The Successes of Guth's Inflationary Theoryp. 195
The Horizon Problem Resolvedp. 195
The Flatness Problem Resolvedp. 196
Problems with Guth's Theory and the New Inflationary Theoryp. 197
Problemsp. 199
Referencesp. 199
The Physics of the Very Early Universep. 201
Introductionp. 201
Cosmic Background Radiationp. 202
Conservation of Photon Numbersp. 206
The Transition Temperature T[subscript t]p. 207
The Photon-to-Baryon Ratiop. 207
The Creation of Matter and Photonsp. 208
A Brief History of the Early Universep. 211
The Planck Epochp. 211
The GUTs Erap. 213
The Inflationary Erap. 213
The Hadron Erap. 214
The Lepton Erap. 215
The Nuclear Erap. 216
The Mystery of Antimatterp. 218
The Dark Matter Problemp. 221
The Primordial Magnetic Fieldsp. 227
Problemsp. 228
Referencesp. 229
Classical Mechanicsp. 231
Newtonian Mechanicsp. 231
The Three Laws of Motionp. 231
The Galilean Transformationp. 233
Newtonian Relativity and Newton's Absolute Spacep. 233
Newton's Law of Gravityp. 235
Gravitational Mass and Inertial Massp. 237
Gravitational Field and Gravitational Potentialp. 238
Gravitational Field Equationsp. 239
Lagrangian Mechanicsp. 240
Hamilton's Principlep. 240
Lagrange's Equations of Motionp. 242
Problemsp. 243
Referencesp. 244
The Special Theory of Relativityp. 245
The Origins of Special Relativityp. 245
The Michelson-Morley Experimentp. 246
The Postulates of the Special Theory of Relativityp. 249
The Lorentz Transformationsp. 251
Relativity of Simultaneity and Causalityp. 253
Time Dilation and Relativity of Co-localityp. 254
Length contractionp. 255
Velocity Transformationp. 257
The Doppler Effectp. 259
Relativistic Space-Time and Minkowski Spacep. 260
Interval ds[superscript 2] as an Invariantp. 262
Four Vectorsp. 265
Four-Velocity and Four-Accelerationp. 268
Four-Momentum Vectorp. 268
The Conservation Laws of Energy and Momentump. 270
Equivalence of Mass and Energyp. 272
Problemsp. 274
Referencesp. 275
Indexp. 277
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780387736297
ISBN-10: 0387736298
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 280
Published: 1st November 2007
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.75
Weight (kg): 1.32