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Introduction to General Relativity: A Course for Undergraduate Students of Physics 1st ed. 2018 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 335 pages, aukštis x plotis: 235x155 mm, weight: 545 g, 36 Illustrations, color; 4 Illustrations, black and white; XVI, 335 p. 40 illus., 36 illus. in color., 1 Paperback / softback
  • Serija: Undergraduate Lecture Notes in Physics
  • Išleidimo metai: 26-Jun-2018
  • Leidėjas: Springer Verlag, Singapore
  • ISBN-10: 9811310890
  • ISBN-13: 9789811310898
Kitos knygos pagal šią temą:
Introduction to General Relativity: A Course for Undergraduate Students of Physics 1st ed. 2018Didesnis paveikslėlis
  • Formatas: Paperback / softback, 335 pages, aukštis x plotis: 235x155 mm, weight: 545 g, 36 Illustrations, color; 4 Illustrations, black and white; XVI, 335 p. 40 illus., 36 illus. in color., 1 Paperback / softback
  • Serija: Undergraduate Lecture Notes in Physics
  • Išleidimo metai: 26-Jun-2018
  • Leidėjas: Springer Verlag, Singapore
  • ISBN-10: 9811310890
  • ISBN-13: 9789811310898
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9789811310898.html
Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action. This method allows the complete theory to be constructed starting from a small number of assumptions, and is the most natural approach in modern theoretical physics. The book begins by reviewing Newtonian mechanics and Newtonian gravity with the Lagrangian formalism and the principle of least action, and then moves to special and general relativity. Most calculations are presented step by step, as is done on the board in class. The book covers recent advances in gravitational wave astronomy and provides a general overview of current lines of research in gravity. It also includes numerous examples and problems in each chapter.
1 Introduction 1(28)
1.1 Special Principle of Relativity
1(2)
1.2 Euclidean Space
3(3)
1.3 Scalars, Vectors, and Tensors
6(2)
1.4 Galilean Transformations
8(3)
1.5 Principle of Least Action
11(2)
1.6 Constants of Motion
13(1)
1.7 Geodesic Equations
14(3)
1.8 Newton's Gravity
17(2)
1.9 Kepler's Laws
19(2)
1.10 Maxwell's Equations
21(2)
1.11 Michelson-Morley Experiment
23(2)
1.12 Towards the Theory of Special Relativity
25(1)
Problems
26(3)
2 Special Relativity 29(18)
2.1 Einstein's Principle of Relativity
29(1)
2.2 Minkow ski Spacetime
30(4)
2.3 Lorentz Transformations
34(4)
2.4 Proper Time
38(1)
2.5 Transformation Rules
39(4)
2.5.1 Superluminal Motion
42(1)
2.6 Example: Cosmic Ray Muons
43(1)
Problems
44(3)
3 Relativistic Mechanics 47(20)
3.1 Action for a Free Particle
47(2)
3.2 Momentum and Energy
49(4)
3.2.1 3-Dimensional Formalism
49(2)
3.2.2 4-Dimensional Formalism
51(2)
3.3 Massless Particles
53(1)
3.4 Particle Collisions
54(1)
3.5 Example: Colliders Versus Fixed-Target Accelerators
55(1)
3.6 Example: The GZK Cut-Off
56(2)
3.7 Multi-body Systems
58(1)
3.8 Lagrangian Formalism for Fields
59(3)
3.9 Energy-Momentum Tensor
62(2)
3.10 Examples
64(2)
3.10.1 Energy-Momentum Tensor of a Free Point-Like Particle
64(1)
3.10.2 Energy-Momentum Tensor of a Perfect Fluid
65(1)
Problems
66(1)
4 Electromagnetism 67(18)
4.1 Action
68(3)
4.2 Motion of a Charged Particle
71(2)
4.2.1 3-Dimensional Formalism
71(2)
4.2.2 4-Dimensional Formalism
73(1)
4.3 Maxwell's Equations in Covariant Form
73(4)
4.3.1 Homogeneous Maxwell's Equations
73(2)
4.3.2 Inhomogeneous Maxwell's Equations
75(2)
4.4 Gauge Invariance
77(1)
4.5 Energy-Momentum Tensor of the Electromagnetic Field
78(1)
4.6 Examples
79(5)
4.6.1 Motion of a Charged Particle in a Constant Uniform Electric Field
79(2)
4.6.2 Electromagnetic Field Generated by a Charged Particle
81(3)
Problems
84(1)
5 Riemannian Geometry 85(22)
5.1 Motivations
85(2)
5.2 Covariant Derivative
87(9)
5.2.1 Definition
88(3)
5.2.2 Parallel Transport
91(4)
5.2.3 Properties of the Covariant Derivative
95(1)
5.3 Useful Expressions
96(2)
5.4 Riemann Tensor
98(6)
5.4.1 Definition
98(2)
5.4.2 Geometrical Interpretation
100(2)
5.4.3 Ricci Tensor and Scalar Curvature
102(1)
5.4.4 Bianchi Identities
103(1)
Problems
104(1)
Reference
105(2)
6 General Relativity 107(16)
6.1 General Covariance
107(3)
6.2 Einstein Equivalence Principle
110(1)
6.3 Connection to the Newtonian Potential
111(2)
6.4 Locally Inertial Frames
113(2)
6.4.1 Locally Minkowski Reference Frames
113(1)
6.4.2 Locally Inertial Reference Frames
114(1)
6.5 Measurements of Time Intervals
115(1)
6.6 Example: GPS Satellites
116(2)
6.7 Non-gravitational Phenomena in Curved Spacetimes
118(3)
Problems
121(2)
7 Einstein's Gravity 123(18)
7.1 Einstein Equations
123(3)
7.2 Newtonian Limit
126(1)
7.3 Einstein-Hilbert Action
127(4)
7.4 Matter Energy-Momentum Tensor
131(4)
7.4.1 Definition
131(1)
7.4.2 Examples
131(3)
7.4.3 Covariant Conservation of the Matter Energy-Momentum Tensor
134(1)
7.5 Pseudo-Tensor of Landau-Lifshitz
135(3)
Problems
138(1)
Reference
139(2)
8 Schwarzschild Spacetime 141(22)
8.1 Spherically Symmetric Spacetimes
141(2)
8.2 Birkhoff's Theorem
143(6)
8.3 Schwarzschild Metric
149(2)
8.4 Motion in the Schwarzschild Metric
151(3)
8.5 Schwarzschild Black Holes
154(3)
8.6 Penrose Diagrams
157(3)
8.6.1 Minkowski Spacetime
157(1)
8.6.2 Schwarzschild Spacetime
158(2)
Problems
160(1)
References
161(2)
9 Classical Tests of General Relativity 163(16)
9.1 Gravitational Redshift of Light
164(2)
9.2 Perihelion Precession of Mercury
166(3)
9.3 Deflection of Light
169(4)
9.4 Shapiro's Effect
173(4)
9.5 Parametrized Post-Newtonian Formalism
177(1)
References
178(1)
10 Black Holes 179(26)
10.1 Definition
179(1)
10.2 Reissner-Nordstr6m Black Holes
180(1)
10.3 Kerr Black Holes
181(12)
10.3.1 Equatorial Circular Orbits
183(6)
10.3.2 Fundamental Frequencies
189(3)
10.3.3 Frame Dragging
192(1)
10.4 No-Hair Theorem
193(1)
10.5 Gravitational Collapse
194(6)
10.5.1 Dust Collapse
196(2)
10.5.2 Homogeneous Dust Collapse
198(2)
10.6 Penrose Diagrams
200(3)
10.6.1 Reissner-Nordstrom Spacetime
200(1)
10.6.2 Kerr Spacetime
201(1)
10.6.3 Oppenheimer-Snyder Spacetime
202(1)
Problems
203(1)
References
204(1)
11 Cosmological Models 205(18)
11.1 Friedmann-Robertson-Walker Metric
205(3)
11.2 Friedmann Equations
208(2)
11.3 Cosmological Models
210(4)
11.3.1 Einstein Universe
211(1)
11.3.2 Matter Dominated Universe
211(2)
11.3.3 Radiation Dominated Universe
213(1)
11.3.4 Vacuum Dominated Universe
214(1)
11.4 Properties of the Friedmann-Robertson-Walker Metric
214(2)
11.4.1 Cosmological Redshift
214(1)
11.4.2 Particle Horizon
215(1)
11.5 Primordial Plasma
216(2)
11.6 Age of the Universe
218(2)
11.7 Destiny of the Universe
220(1)
Problems
221(1)
Reference
221(2)
12 Gravitational Waves 223(34)
12.1 Historical Overview
223(2)
12.2 Gravitational Waves in Linearized Gravity
225(6)
12.2.1 Harmonic Gauge
226(2)
12.2.2 Transverse-Traceless Gauge
228(3)
12.3 Quadrupole Formula
231(3)
12.4 Energy of Gravitational Waves
234(4)
12.5 Examples
238(5)
12.5.1 Gravitational Waves from a Rotating Neutron Star
238(3)
12.5.2 Gravitational Waves from a Binary System
241(2)
12.6 Astrophysical Sources
243(4)
12.6.1 Coalescing Black Holes
244(1)
12.6.2 Extreme-Mass Ratio Inspirals
245(2)
12.6.3 Neutron Stars
247(1)
12.7 Gravitational Wave Detectors
247(7)
12.7.1 Resonant Detectors
251(1)
12.7.2 Interferometers
251(2)
12.7.3 Pulsar Timing Arrays
253(1)
Problem
254(1)
References
254(3)
13 Beyond Einstein's Gravity 257(10)
13.1 Spacetime Singularities
257(2)
13.2 Quantization of Einstein's Gravity
259(2)
13.3 Black Hole Thermodynamics and Information Paradox
261(2)
13.4 Cosmological Constant Problem
263(2)
Problem
265(1)
References
265(2)
Appendix A: Algebraic Structures 267(6)
Appendix B: Vector Calculus 273(4)
Appendix C: Differentiable Manifolds 277(8)
Appendix D: Ellipse Equation 285(2)
Appendix E: Mathematica Packages for Tensor Calculus 287(4)
Appendix F: Interior Solution 291(8)
Appendix G: Metric Around a Slow-Rotating Massive Body 299(4)
Appendix H: Friedmann-Robertson-Walker Metric 303(4)
Appendix I: Suggestions for Solving the Problems 307(24)
Subject Index 331
Cosimo Bambi is Xie Xide Junior Chair Professor at the Department of Physics at Fudan University (Shanghai, China) and a Humboldt Fellow at Eberhard Karls Universität Tübingen (Tübingen, Germany). He received his PhD from Ferrara University (Italy) in 2007, and was a postdoc at Wayne State University (Michigan), IPMU at The University of Tokyo (Japan), and at LMU Munich (Germany). He moved to Fudan University at the end of 2012 under the Thousand Young Talents Program. In 2016, he was awarded with a JSPS fellowship to visit Japan. In 2018, he received the Xu Guangqi Award (for the best Italian researcher in China). He regularly serves as referee for journals like PRL, ApJ, JHEP, JCAP, etc. and as proposal reviewer for the Chang Jiang Scholars Program (China), Czech Science Foundation (Czech Republic), German Research Foundation (Germany), and National Research Foundation (South Africa). His research interests cover several areas in gravity, cosmology, and high-energy astrophysics. He has published more than 100 papers on refereed journals as first or corresponding author, has over 3,000 citations, and his h-index is 34. He has authored two books, and edited one volume (in ASSL) with Springer.