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College Course on Relativity and Cosmology [Kietas viršelis]

4.00/5 (1 ratings by Goodreads)
(Professor Emeritus, University of Missouri - St. Louis)
  • Formatas: Hardback, 306 pages, aukštis x plotis x storis: 248x194x21 mm, weight: 802 g, 71 b/w illustrations
  • Išleidimo metai: 18-Jun-2015
  • Leidėjas: Oxford University Press
  • ISBN-10: 0199693404
  • ISBN-13: 9780199693405
Kitos knygos pagal šią temą:
College Course on Relativity and CosmologyDidesnis paveikslėlis
  • Formatas: Hardback, 306 pages, aukštis x plotis x storis: 248x194x21 mm, weight: 802 g, 71 b/w illustrations
  • Išleidimo metai: 18-Jun-2015
  • Leidėjas: Oxford University Press
  • ISBN-10: 0199693404
  • ISBN-13: 9780199693405
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780199693405.html
Raktažodžiai:
This advanced undergraduate text introduces Einstein's general theory of relativity. The topics covered include geometric formulation of special relativity, the principle of equivalence, Einstein's field equation and its spherical-symmetric solution, as well as cosmology. An emphasis is placed on physical examples and simple applications without the full tensor apparatus. It begins by examining the physics of the equivalence principle and looks at how it inspired Einstein's idea of curved spacetime as the gravitational field. At a more mathematically accessible level, it provides a metric description of a warped space, allowing the reader to study many interesting phenomena such as gravitational time dilation, GPS operation, light deflection, precession of Mercury's perihelion, and black holes. Numerous modern topics in cosmology are discussed from primordial inflation and cosmic microwave background to the dark energy that propels an accelerating universe.

Building on Cheng's previous book, 'Relativity, Gravitation and Cosmology: A Basic Introduction', this text has been tailored to the advanced student. It concentrates on the core elements of the subject making it suitable for a one-semester course at the undergraduate level. It can also serve as an accessible introduction of general relativity and cosmology for those readers who want to study the subject on their own. The proper tensor formulation of Einstein's field equation is presented in an appendix chapter for those wishing to glimpse further at the mathematical details.

Recenzijos

The writing is authoritative and lucid, and the author follows a solid development of the special and general theories of relativity before introducing contemporary cosmology. The presentation is streamlined in terms of selection of topics, but this allows a comprehensive discussion of the subject matter. ... Recommended. * J. R. Burciaga, CHOICE *

1 Introduction
1(10)
1.1 Relativity as a coordinate symmetry
2(6)
1.1.1 Coordinate transformations
3(3)
1.1.2 The principle of relativity
6(2)
1.2 Einstein and relativity
8(3)
1.2.1 The new kinematics
8(2)
1.2.2 GR as a field theory of gravitation
10(1)
Review questions
10(1)
2 Special Relativity: The New Kinematics
11(20)
2.1 Einstein's two postulates and Lorentz transformation
12(7)
2.1.1 Relativity of simultaneity and the new conception of time
13(2)
2.1.2 Coordinate-dependent time leads to Lorentz transformation
15(4)
2.2 Physics implications of Lorentz transformation
19(6)
2.2.1 Time dilation and length contraction
19(3)
2.2.2 The invariant interval and proper time
22(3)
2.3 Two counterintuitive scenarios as paradoxes
25(6)
Review questions
29(2)
3 Special Relativity: Flat Spacetime
31(26)
3.1 Geometric formulation of relativity
32(2)
3.2 Tensors in special relativity
34(17)
3.2.1 Generalized coordinates: bases and the metric
34(4)
3.2.2 Velocity and momentum 4-vectors
38(7)
3.2.3 Electromagnetic field 4-tensor
45(4)
3.2.4 The energy--momentum--stress 4-tensor for a field system
49(2)
3.3 The spacetime diagram
51(6)
3.3.1 Invariant regions and causal structure
52(1)
3.3.2 Lorentz transformation in the spacetime diagram
53(3)
Review questions
56(1)
4 Equivalence of Gravitation and Inertia
57(22)
4.1 Seeking a relativistic theory of gravitation
58(2)
4.1.1 Newtonian potential: a summary
58(1)
4.1.2 Einstein's motivation for general relativity
59(1)
4.2 The equivalence principle: from Galileo to Einstein
60(3)
4.2.1 Inertial mass vs. gravitational mass
60(1)
4.2.2 Einstein: "my happiest thought"
61(2)
4.3 EP leads to gravitational time dilation and light deflection
63(16)
4.3.1 Gravitational redshift and time dilation
63(7)
4.3.2 Relativity and the operation of GPS
70(3)
4.3.3 The EP calculation of light deflection
73(2)
4.3.4 Energetics of light transmission in a gravitational field
75(3)
Review questions
78(1)
5 General Relativity as a Geometric Theory of Gravity
79(20)
5.1 Metric description of a curved manifold
80(11)
5.1.1 Gaussian coordinates and the metric tensor
80(5)
5.1.2 The geodesic equation
85(5)
5.1.3 Local Euclidean frames and the flatness theorem
90(1)
5.2 From the equivalence principle to a metric theory of gravity
91(4)
5.2.1 Curved spacetime as gravitational field
92(2)
5.2.2 GR as a field theory of gravitation
94(1)
5.3 Geodesic equation as the GR equation of motion
95(4)
5.3.1 The Newtonian limit
96(2)
Review questions
98(1)
6 Einstein Equation and its Spherical Solution
99(34)
6.1 Curvature: a short introduction
101(5)
6.2 Tidal gravity and spacetime curvature
106(3)
6.2.1 Tidal forces---a qualitative discussion
106(1)
6.2.2 Deviation equations and tidal gravity
107(2)
6.3 The GR field equation
109(5)
6.3.1 Einstein curvature tensor
109(2)
6.3.2 Einstein field equation
111(1)
6.3.3 Gravitational waves
112(2)
6.4 Geodesies in Schwarzschild spacetime
114(19)
6.4.1 The geometry of a spherically symmetric spacetime
117(4)
6.4.2 Curved spacetime and deflection of light
121(3)
6.4.3 Precession of Mercury's orbit
124(7)
Review questions
131(2)
7 Black Holes
133(23)
7.1 Schwarzschild black holes
134(10)
7.1.1 Time measurements around a black hole
135(2)
7.1.2 Causal structure of the Schwarzschild surface
137(5)
7.1.3 Binding energy to a black hole can be extremely large
142(2)
7.2 Astrophysical black holes
144(4)
7.2.1 More realistic black holes
144(3)
7.2.2 Black holes in our universe
147(1)
7.3 Black hole thermodynamics and Hawking radiation
148(8)
7.3.1 Laws of black hole mechanics and thermodynamics
149(1)
7.3.2 Hawking radiation: quantum fluctuation around the horizon
150(5)
Review questions
155(1)
8 The General Relativistic Framework for Cosmology
156(31)
8.1 The cosmos observed
157(10)
8.1.1 The expanding universe and its age
158(5)
8.1.2 Mass/energy content of the universe
163(4)
8.2 The homogeneous and isotropic universe
167(5)
8.2.1 Robertson--Walker metric in comoving coordinates
168(2)
8.2.2 Hubble's law follows from the cosmological principle
170(2)
8.3 Time evolution in FLRW cosmology
172(9)
8.3.1 Friedmann equations and their simple interpretation
172(6)
8.3.2 Time evolution of model universes
178(3)
8.4 The cosmological constant Δ
181(6)
8.4.1 Δ as vacuum energy and pressure
182(3)
8.4.2 Δ-dominated universe expands exponentially
185(1)
Review questions
186(1)
9 Big Bang Thermal Relics
187(23)
9.1 The thermal history of the universe
188(5)
9.1.1 Scale dependence of radiation temperature
188(2)
9.1.2 Different thermal equilibrium stages
190(3)
9.2 Primordial nucleosynthesis
193(4)
9.3 Photon decoupling and cosmic microwave background
197(13)
9.3.1 Universe became transparent to photons
197(7)
9.3.2 CMB anisotropy as a baby picture of the universe
204(5)
Review questions
209(1)
10 Inflation and the Accelerating Universe
210(26)
10.1 The cosmic inflation epoch
211(12)
10.1.1 Initial condition problems of FLRW cosmology
211(2)
10.1.2 The inflationary scenario
213(9)
10.1.3 Eternal inflation and the multiverse
222(1)
10.2 The accelerating universe in the present era
223(11)
10.2.1 Dark energy and its effect
223(1)
10.2.2 Distant supernovae and the 1998 discovery
224(7)
10.2.3 The mysterious physical origin of dark energy
231(3)
10.3 ΔCDM cosmology as the standard model
234(2)
Review questions
235(1)
11 Tensor Formalism for General Relativity
236(23)
11.1 Covariant derivatives and parallel transport
238(7)
11.1.1 Derivatives in a curved space and Christoffel symbols
239(4)
11.1.2 Parallel transport and geodesies as straight lines
243(2)
11.2 Riemann curvature tensor
245(8)
11.2.1 Parallel transport of a vector around a closed path
246(3)
11.2.2 Equation of geodesic deviation
249(3)
11.2.3 Bianchi identity and the Einstein tensor
252(1)
11.3 GR tensor equations
253(6)
11.3.1 The principle of general covariance
254(1)
11.3.2 Einstein field equation
255(2)
Review questions
257(2)
Appendix A Keys to Review Questions 259(11)
Appendix B Hints for Selected Exercises 270(6)
Appendix C Glossary of Symbols and Acronyms 276(5)
References and Bibliography 281(4)
Index 285
Ta-Pei Cheng is a particle physics theorist. After graduating from Dartmouth College, he obtained his PhD at Rockefeller University with the noted physicist and Einstein biographer Abraham Pais. During 1973-2007 he was on the faculty at University of Missouri - St. Louis, where he now holds the rank of Professor Emeritus. Starting the early 1980's Oxford University Press has published a number of his books, the most recent one being "Einstein's Physics: Atoms, Quanta, and Relativity - Derived, Explained, and Appraised".