Hardcover
Published: 1st November 2007
ISBN: 9780387736297
Number Of Pages: 280
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 Author | p. vii |
Preface | p. ix |
Basic Ideas of General Relativity | p. 1 |
Inadequacy of Special Relativity | p. 1 |
Einstein's Principle of Equivalence | p. 3 |
Immediate Consequences of the Principle of Equivalence | p. 7 |
The Bending of a Light Beam | p. 7 |
Gravitational Shift of Spectral Lines (Gravitational Redshift) | p. 8 |
The Curved Space-Time Concept | p. 8 |
The Principle of General Covariance | p. 12 |
Distance and Time Intervals | p. 13 |
Problems | p. 15 |
References | p. 17 |
Curvilinear Coordinates and General Tensors | p. 19 |
Curvilinear Coordinates | p. 19 |
Parallel Displacement and Covariant Differentiation | p. 23 |
Symmetry Properties of the Christoffel Symbols | p. 27 |
Christoffel Symbols and the Metric Tensor | p. 28 |
Geodesics | p. 29 |
The Stationary Property of Geodesics | p. 30 |
The Curvature Tensor | p. 32 |
The Condition for Flat Space | p. 36 |
Geodesic Deviation | p. 37 |
Laws of Physics in Curved Spaces | p. 38 |
The Metric Tensor and the Classical Gravitational Potential | p. 39 |
Some Useful Calculation Tools | p. 40 |
Problems | p. 43 |
References | p. 44 |
Einstein's Law of Gravitation | p. 45 |
Introduction (Summary of General Principles) | p. 45 |
A Heuristic Derivation of Einstein's Equations | p. 46 |
Vacuum Field Equations | p. 46 |
Field Equations Where Matter is Present in Space | p. 48 |
Energy-Momentum Tensor | p. 51 |
Gravitational Radiation | p. 52 |
Problems | p. 54 |
References | p. 54 |
The Schwarzschild Solution | p. 55 |
The Schwarzschild Metric | p. 55 |
The Schwarzschild Solution of the Vacuum Field Equations | p. 56 |
Schwarzschild Geodesics | p. 60 |
Quasiuniform Gravitational Field | p. 62 |
Problems | p. 63 |
References | p. 63 |
Experimental Tests of Einstein's Theory | p. 65 |
Precession of the Perihelion of Mercury | p. 65 |
Deflection of Light Rays in a Gravitational Field | p. 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 |
Problems | p. 79 |
References | p. 79 |
The Physics of Black Holes | p. 81 |
The Schwarzschild Black Hole | p. 81 |
Inside a Black Hole | p. 84 |
How a Black Hole May Form | p. 86 |
The Kerr-Newman Black Hole | p. 89 |
Energy Extraction from a Rotating Black Hole: The Penrose Process | p. 92 |
The Area Theorem | p. 93 |
Energy Extraction from Two Coalescing Black Holes | p. 94 |
Thermodynamics of Black Holes | p. 95 |
Quantum Mechanics of Black Holes: Hawking Radiation | p. 97 |
The Detection of Black Holes | p. 101 |
Detection of Stellar-Mass Black Holes | p. 101 |
Supermassive Black Holes in the Centers of Galaxies | p. 104 |
Intermediate-Mass Black Holes | p. 106 |
How Do Electrical and Gravitational Fields Get Out of Black Holes? | p. 106 |
Black Holes and Particle Physics | p. 107 |
Problems | p. 108 |
References | p. 109 |
Introduction to Cosmology | p. 111 |
Introduction | p. 111 |
The Development of Western Cosmological Concepts | p. 112 |
Ancient Greece | p. 112 |
The Renaissance of Cosmology | p. 113 |
Newton and the Infinite Universe | p. 114 |
Newton's Law of Gravity and a Nonstationary Universe | p. 115 |
Olbers' Paradox | p. 118 |
The Discovery of the Expansion of the Universe | p. 119 |
The Big Bang | p. 123 |
The Microwave Background Radiation | p. 124 |
Additional Evidence for the Big Bang | p. 128 |
Problems | p. 130 |
References | p. 131 |
Big Bang Models | p. 133 |
The Cosmic Fluid and Fundamental Observers | p. 133 |
Properties of the Robertson-Walker Metric | p. 135 |
Cosmic Dynamics and Friedmann's Equations | p. 139 |
The Solutions of Friedmann's Equations | p. 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 Universe | p. 148 |
The Beginning, the End, and Time's Arrow | p. 152 |
An Accelerating Universe? | p. 156 |
The Cosmological Constant | p. 158 |
Problems | p. 161 |
References | p. 161 |
Particles, Forces, and Unification of Forces | p. 163 |
Particles | p. 163 |
Spin | p. 163 |
Fermions | p. 164 |
Bosons | p. 165 |
Hadrons and Leptons | p. 165 |
Quarks | p. 167 |
Quark Colors | p. 168 |
Quark Confinement | p. 169 |
Fundamental Interactions and Conservation Laws | p. 171 |
Spontaneous Symmetry Breaking | p. 177 |
Unification of Forces (Interactions) | p. 180 |
The Negative Vacuum Pressure | p. 184 |
References | p. 186 |
The Inflationary Universe | p. 187 |
The Flatness Problem | p. 187 |
The Horizon Problem | p. 188 |
Alan Guth's Inflationary Theory | p. 191 |
The Successes of Guth's Inflationary Theory | p. 195 |
The Horizon Problem Resolved | p. 195 |
The Flatness Problem Resolved | p. 196 |
Problems with Guth's Theory and the New Inflationary Theory | p. 197 |
Problems | p. 199 |
References | p. 199 |
The Physics of the Very Early Universe | p. 201 |
Introduction | p. 201 |
Cosmic Background Radiation | p. 202 |
Conservation of Photon Numbers | p. 206 |
The Transition Temperature T[subscript t] | p. 207 |
The Photon-to-Baryon Ratio | p. 207 |
The Creation of Matter and Photons | p. 208 |
A Brief History of the Early Universe | p. 211 |
The Planck Epoch | p. 211 |
The GUTs Era | p. 213 |
The Inflationary Era | p. 213 |
The Hadron Era | p. 214 |
The Lepton Era | p. 215 |
The Nuclear Era | p. 216 |
The Mystery of Antimatter | p. 218 |
The Dark Matter Problem | p. 221 |
The Primordial Magnetic Fields | p. 227 |
Problems | p. 228 |
References | p. 229 |
Classical Mechanics | p. 231 |
Newtonian Mechanics | p. 231 |
The Three Laws of Motion | p. 231 |
The Galilean Transformation | p. 233 |
Newtonian Relativity and Newton's Absolute Space | p. 233 |
Newton's Law of Gravity | p. 235 |
Gravitational Mass and Inertial Mass | p. 237 |
Gravitational Field and Gravitational Potential | p. 238 |
Gravitational Field Equations | p. 239 |
Lagrangian Mechanics | p. 240 |
Hamilton's Principle | p. 240 |
Lagrange's Equations of Motion | p. 242 |
Problems | p. 243 |
References | p. 244 |
The Special Theory of Relativity | p. 245 |
The Origins of Special Relativity | p. 245 |
The Michelson-Morley Experiment | p. 246 |
The Postulates of the Special Theory of Relativity | p. 249 |
The Lorentz Transformations | p. 251 |
Relativity of Simultaneity and Causality | p. 253 |
Time Dilation and Relativity of Co-locality | p. 254 |
Length contraction | p. 255 |
Velocity Transformation | p. 257 |
The Doppler Effect | p. 259 |
Relativistic Space-Time and Minkowski Space | p. 260 |
Interval ds[superscript 2] as an Invariant | p. 262 |
Four Vectors | p. 265 |
Four-Velocity and Four-Acceleration | p. 268 |
Four-Momentum Vector | p. 268 |
The Conservation Laws of Energy and Momentum | p. 270 |
Equivalence of Mass and Energy | p. 272 |
Problems | p. 274 |
References | p. 275 |
Index | p. 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 15.88
x 1.91
Weight (kg): 0.54