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Introduction to General Relativity [Kõva köide]

(University of Kent, Canterbury)
  • Formaat: Hardback, 453 pages, kõrgus x laius x paksus: 252x196x22 mm, kaal: 1140 g, Worked examples or Exercises; 1 Halftones, unspecified
  • Ilmumisaeg: 11-Jun-2009
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521845637
  • ISBN-13: 9780521845632
Teised raamatud teemal:
  • Formaat: Hardback, 453 pages, kõrgus x laius x paksus: 252x196x22 mm, kaal: 1140 g, Worked examples or Exercises; 1 Halftones, unspecified
  • Ilmumisaeg: 11-Jun-2009
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521845637
  • ISBN-13: 9780521845632
Teised raamatud teemal:
A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Password protected solutions for instructors are available at www.cambridge.org/9780521845632.

Student-friendly, well illustrated textbook for advanced undergraduate and beginning graduate students in physics and mathematics.

Arvustused

'This superb and spirited modern introduction to Einstein's theory of gravitation covers all of the essential topics with admirable clarity. A penetrating discussion of the basic concepts of the theory is followed by a wonderfully lucid development of the mathematical formalism using modern differential geometry. Ample illustrations and problems enhance and complement the text; moreover, a generous list of references is provided at the end of each chapter for further reading. This scholarly yet accessible textbook is highly recommended for a course on general relativity.' Bahram Mashhoon, University of Missouri 'This book offers a lucid introduction to Einstein's theory of gravitation which is finally part of mainstream physics in many undergraduate final year options. The style is pedagogic and notable for a gentle but concise introduction to modern calculational tools in applied differential geometry along with traditional tensor calculus. The student will surely find the careful attention to detail in the many explicit computations of advanced topics (such as action principles, pseudo-tensors, gravito-magnetism and the Dirac equation in a curved space-time) of immense help in developing an understanding of general relativity. The book provides a welcome fresh approach for all students wishing to take the subject further.' Robin Tucker, Lancaster University 'Lewis Ryder, an exceptionally fine teacher has written a lucid account of the subject, suitable for undergraduates familiar with the special theory. In this handsomely produced volume, Ryder develops the subject from its simple principles into a mathematical edifice of unsurpassed mathematical beauty. I would recommend anyone teaching this subject to take a look at this text, a strong candidate for the best treatment on the market. extremely thorough and clear this could emerge as a market leader in a crowded field.' The Times Higher Education Supplement 'This modern and inspiring textbook is highly recommended not only for a course on general relativity, but also to those who wish to learn this exciting subject by a self-study.' Annalen der Physik 'On the whole, the selection of the material and the general structure of the book is quite traditional. The two notable exceptions are the careful exposition of gravitomagnetism and the informative discussion of the gauge approach to gravity; both topics are not usually included in textbooks on general relativity I enjoyed reading this book [ a lot]. Written with great care and accuracy in a lively and beautiful style [ it] will be undoubtedly appreciated by students, researchers and lecturers.' General Relativity and Gravitation

Muu info

Student-friendly, well illustrated textbook for advanced undergraduate and beginning graduate students in physics and mathematics.
Preface xiii
Notation, important formulae and physical constants xiv
Introduction
1(17)
The Need for a theory of gravity
1(2)
Gravitation and inertia: the Equivalence Principle in mechanics
3(6)
The Equivalence Principle and optics
9(5)
Curved surfaces
14(2)
Further reading
16(1)
Problems
16(2)
Special Relativity, non-inertial effects and electromagnetism
18(29)
Special Relativity: Einstein's train
18(8)
Twin paradox: accelerations
26(3)
Rotating frames: the Sagnac effect
29(5)
Inertia: Newton versus Mach
34(2)
Thomas precession
36(4)
Electromagnetism
40(3)
Principle of General Covariance
43(2)
Further reading
45(1)
Problems
46(1)
Differential geometry I: vectors, differential forms and absolute differentiation
47(65)
Space-time as a differentiable manifold
47(2)
Vectors and vector fields
49(6)
One-forms
55(6)
Tensors
61(4)
Differential forms: Hodge duality
65(7)
Exterior derivative operator: generalised Stokes' theorem
72(5)
Maxwell's equations and differential forms
77(2)
Metric tensor
79(7)
Absolute differentiation: connection forms
86(7)
Parallel transport
93(4)
Some relations involving connection coefficients
97(5)
Examples
102(5)
General formula for connection coefficients
107(3)
Further reading
110(1)
Problems
110(2)
Differential geometry II: geodesics and curvature
112(25)
Autoparallel curves and geodesics
112(7)
Geodesic coordinates
119(2)
Curvature
121(4)
Symmetries of the Riemann tensor
125(1)
Ricci tensor and curvature scalar
126(3)
Curvature 2-form
129(3)
Geodesic deviation
132(2)
Bianchi identities
134(1)
Further reading
135(1)
Problems
135(2)
Einstein field equations, the Schwarzschild solution and experimental tests of General Relativity
137(43)
Newtonian limit
137(2)
Einstein field equations
139(7)
Schwarzschild solution
146(5)
Time dependence and spherical symmetry: Birkhoff's theorem
151(3)
Gravitational red-shift
154(4)
Geodesics in Schwarzschild space-time
158(2)
Precession of planetary orbits
160(2)
Deflection of light
162(2)
Note on PPN formalism
164(1)
Gravitational lenses
165(4)
Radar echoes from planets
169(4)
Radial motion in a Schwarzschild field: black holes - frozen stars
173(3)
A gravitational clock effect
176(2)
Further reading
178(1)
Problems
178(2)
Gravitomagnetic effects: gyroscopes and clocks
180(47)
Linear approximation
180(11)
Precession of gyroscopes: the Lense-Thirring effect
191(9)
Gravitomagnetism
200(4)
Gravitomagnetic clock effect
204(3)
Fermi---Walker transport: tetrad formalism
207(4)
Lie derivatives, Killing vectors and groups of motion
211(8)
Static and stationary space-times
219(4)
Killing vectors and conservation laws
223(2)
Further reading
225(1)
Problems
226(1)
Gravitational collapse and black holes
227(68)
The interior Schwarzschild solution and the Tolman---Oppenheimer-Volkoff equation
228(9)
Energy density and binding energy
237(6)
Degenerate stars: white dwarfs and neutron stars
243(8)
Schwarzschild orbits: Eddington-Finkelstein coordinates
251(4)
Kruskal-Szekeres coordinates
255(4)
Einstein-Rosen bridge and wormholes
259(2)
Conformal treatment of infinity: Penrose diagrams
261(4)
Rotating black holes: Kerr solution
265(6)
The ergosphere and energy extraction from a black hole
271(9)
Surface gravity
280(7)
Thermodynamics of black holes and further observations
287(4)
Global matters: singularities, trapped surfaces and Cosmic Censorship
291(2)
Further reading
293(1)
Problems
294(1)
Action principle, conservation laws and the Cauchy problem
295(15)
Gravitational action and field equations
295(5)
Energy-momentum pseudotensor
300(4)
Cauchy problem
304(5)
Further reading
309(1)
Problems
309(1)
Gravitational radiation
310(31)
Weak field approximation
310(7)
Radiation from a rotating binary source
317(11)
Parallels between electrodynamics and General Relativity: Petrov classification
328(12)
Further reading
340(1)
Problems
340(1)
Cosmology
341(51)
Brief description of the Universe
341(3)
Robertson-Walker metric
344(11)
Hubble's law and the cosmological red-shift
355(2)
Horizons
357(3)
Luminosity-red-shift relation
360(3)
Dynamical equations of cosmology
363(8)
Friedmann models and the cosmological constant
371(4)
Cosmic background radiation
375(2)
Brief sketch of the early Universe
377(6)
The inflationary universe and the Higgs mechanism
383(8)
Further reading
391(1)
Problems
391(1)
Gravitation and field theory
392(33)
Electrodynamics as an abelian gauge theory
394(6)
Non-abelian gauge theories
400(9)
Gauging Lorentz symmetry: torsion
409(7)
Dirac equation in Schwarzschild space-time
416(2)
Five dimensions: gravity plus electromagnetism
418(5)
Further reading
423(1)
Problems
424(1)
References 425(14)
Index 439
Lewis Ryder is an Honorary Senior Lecturer in Physics at the University of Kent, UK. His research interests are in geometrical aspects of particle theory and its parallels with general relativity.