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

Gravity, Black Holes, and the Very Early Universe: An Introduction to General Relativity and…

byTai L. Chow

Hardcover | October 26, 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.

About The Author

Tai L. Chow is Professor of Physics at California State University, Stanislaus. He has written a successful text on Mathematical Methods with Cambridge University Press: Chow, Mathematical Methods for Physicists: A Concise Introduction (Cambridge, ISBN 0521655447 , 555 pp., Hardcover, $58.00 [Hardcover: $120.00], 7/2000)

Details & Specs

Title:Gravity, Black Holes, and the Very Early Universe: An Introduction to General Relativity and…Format:HardcoverDimensions:296 pages, 9.25 × 6.1 × 0.09 inPublished:October 26, 2007Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387736298

ISBN - 13:9780387736297

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Table of Contents

PrefaceChapter 1 Basic Ideas of General Relativity1.1 Inadequacy of special relativity and Mach's principle1.2 Einstein's principle of equivalence1.3 Immediate consequences of the principle of equivalenceThe bending of a light beamGravitational shift of spectral lines1.4 The curved spacetime concept1.5 The principle of general covariance1.6 Distance and time intervalsReferencesProblemsChapter 2 Curvilinear Coordinates and General Tensors2.1 Curvilinear coordinates2.2 Parallel displacement and covariant differentiation2.3 Symmetry properties of the Christoffel symbols2.4 Christoffel symbols and the metric tensor2.5 The Geodesics2.6 The stationary property of geodesics2.7 The curvature tensor2.8 Geodesic deviation2.9 Laws of physics in curved space2.10 The metric tensor and the classical gravitational potential2.11 Some useful calculation aidsReferencesProblemsChapter 3 Einstein's Law of Gravitation3-1 Introduction (summary of general principles)3-2 A heuristic derivation of Einstein's equations3-3 Energy-momentum tensorReferencesProblemsChapter 4 The Schwarzschild Solution4-1 The Schwarzschild metric4-2 The Schwarzschild solution of the vacuum field equationsThe gravitational redshift4-3 Isotropic coordinates4-4 Schwarzschild geodesic4-5 First integrals of the Schwarzschild solutions4-6 Quasiuniform gravitational fieldReferencesProblemsChapter 5 Experimental Tests of Einstein's Theory5-1 Precession of the perihelion of Mercury5-2 Deflection of light rays in a gravitational field5-3 Light retardation (The Shaoiro experiment)5-4 Test of gravitational radiation (Hulse-Taylor's measurement ofdecay of the orbit of the binary pulsar PSR-1913+16)ReferencesProblemsChapter 6 The Physics of Black Holes6-1 The Schwarzschild black holes6-2 Inside a black hole6-3 How a black hole forms6-4 The Kerr-Newmann black holesEnergy extraction from a rotating blackhole: the Penrose processThe area theoremEnergy extraction from two coalescing black holes6-5 Thermodynamics of black holesQuantum mechanics of black holes; Hawking radiation6-6 The detection of black holesa. Detection of stellar-mass black holesb. Supermassive black holes in the centers of galaxiesc. Intermediate-mass black holes6-7 How do electric and gravitational fields get out of black holes?6-8 Black holes and particle PhysicsReferencesProblemsChapter 7 Introduction to Cosmology7-1 Introduction7-2 A little history on the development of western cosmological conceptsAncient GreeceThe renaissance of cosmologyNewton and infinite universeNewton's law pf gravity predicts a non-stationary universeOlbers's paradox7-3 The discovery of expansion of the universe7-4 The Big BangCosmological redshift7-5 The microwave background radiation7-6 Additional evidence for the Big BangReferencesProblemsChapter 8 Big Bang Models8-1 The cosmic fluid and fundamental observers8-2 Properties of the Robertson-Walker metric8-3 Cosmic dynamics; Friedmann's equations8-4 The solutions of Friedmann's equations A. Flat model (k = 0) B. Closed model (k = 1) C. Open model (k = -1)8-5 Dark matter and the fate of the universe8-6 The Beginning, the end, and time's arrow8-7 An accelerating universe?8-8 The cosmological constantReferencesProblemsChapter 9 Particles, Forces, and Unification of Forces9-1 particlesSpin, fermions, and bosonsHarons and leptonsQuarksQuark colors and quark confinement9-2 Fundamental forces (interactions)Conservation laws9-3 Spontaneous symmetry breaking9-4 Unification of forces9-5 The vacuum pressure is negativeReferencesChapter 10 The Inflationary Universe10-1 The flatness problem10-2 The horizon problem10-3 Alan Guth's inflationary scenario10-4 The successes of Guth's inflationary theoryThe flatness problem is resolvedThe horizon problem is resolved10-5 Problems with Guth's theory and new inflationary theoryReferenceProblemsChapter 11 Exploring the Very Early Universe11-1 Introduction11-2 Cosmic background radiationThe transition temperature TtConservation of photon numbersThe photon to baryon ratio11-3 The creation of matter and photons11-4 A brief history of the early universeThe Planck epochThe GUT's eraThe inflationary eraThe hadron eraThe lepton eraThe nuclear era11-5 Mystery of the antimatter11-6 The dark matter problem11-7 The primordial magnetic fieldsReferencesProblems

Editorial Reviews

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)