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General Relativity: A First Examination Second Edition [Pehme köide]

(Virginia Tech, Usa)
  • Formaat: Paperback / softback, 240 pages
  • Ilmumisaeg: 14-Aug-2020
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811221081
  • ISBN-13: 9789811221088
Teised raamatud teemal:
  • Formaat: Paperback / softback, 240 pages
  • Ilmumisaeg: 14-Aug-2020
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811221081
  • ISBN-13: 9789811221088
Teised raamatud teemal:

This textbook is suitable for a one-semester introduction to General Relativity for advanced undergraduates in physics and engineering. The book is concise so that the entire material can be covered in the one-semester time frame. Many of the calculations are done in detail, without difficult mathematics, to help the students. Though concise, the theory development is lucid and the readers are exposed to possible analytic calculations. In the second edition, the famous twin paradox with acceleration is solved in full from the accelerated observer's frame. The findings of the Event Horizon Telescope (EHT) collaboration, who captured the first ever image of a black hole, are discussed in detail. The geodetic and frame drag precessions of gyroscopes in orbit about a rotating Earth are worked out and the Gravity Probe B (GPB) experiment is discussed. Also in the second edition are some new exercise problems. Resources are provided to instructors who adopt this textbook for their courses. Adopting instructors can print and copy portions of these resources solely for their teaching needs. All instructional resources are furnished for informational use only, and are subject to change without notice.

Preface vii
Acknowledgments ix
1 Review Of Special Relativity
1(16)
1.1 Introduction
1(4)
1.2 Lorentz Transform
5(2)
1.3 Physics Consequences
7(4)
1.4 Spacetime Diagrams
11(6)
2 Vectors And Tensors In Spacetime
17(24)
2.1 Metric Tensor
17(1)
2.2 Vector Transforms
18(3)
2.3 Tensor Transforms
21(1)
2.4 Forming Other Vectors
22(1)
2.5 Twin Problem Revisited
23(3)
2.6 Momentum and Energy
26(1)
2.7 Doppler Shift
26(2)
2.8 Gravity Affects Time
28(1)
2.9 The Pound--Rebka Experiment
29(2)
2.10 Global Positioning System
31(4)
2.11 Tensor Equations
35(6)
3 Covariant Differentiation, Equations Of Motion
41(14)
3.1 Differentiation of Invariants and Vectors
41(4)
3.2 Differentiation of Tensors
45(1)
3.3 Gravity and the Locally Inertial Frame
46(2)
3.4 Local Flatness Theorem
48(2)
3.5 GR Equations of Motion
50(5)
4 Curvature
55(14)
4.1 Geodesies
55(4)
4.2 Parallel Transport
59(4)
4.3 Curvature Tensors
63(1)
4.4 Ricci Tensor, Bianchi Identity, Einstein Tensor
64(5)
5 Gravity And General Relativity
69(22)
5.1 Review of Newtonian Gravity
69(2)
5.2 Weak Gravity in GR
71(2)
5.3 Gravitational Red Shift
73(2)
5.4 Einstein's Field Equations
75(1)
5.5 Schwarzschild Solution
76(3)
5.6 Conserved Quantities: Massive Particles
79(1)
5.7 The Twin Problem From the Rocket Observer's View
80(11)
6 Classic Solar System Tests Of General Relativity
91(16)
6.1 Equations of Motion
91(3)
6.2 Orbit Equations
94(1)
6.3 Light Deflection
95(3)
6.4 Perihelia Advance
98(4)
6.5 Radar Signal Delay
102(5)
7 Gravitational Waves
107(34)
7.1 The Weak Gravity Wave Equation
107(3)
7.2 Plane Waves
110(2)
7.3 The Graviton
112(2)
7.4 Gravity Wave Detection: LIGO Experiment
114(3)
7.5 Wave Equation Solution With Sources
117(2)
7.6 The Energy--Momentum Tensor
119(2)
7.7 Quadrupole Radiation
121(2)
7.8 Gravity Wave Flux and Power
123(7)
7.9 Binary Neutron Star System Radiation
130(11)
8 Black Holes And Kerr Space
141(42)
8.1 Static Black Holes
141(5)
8.2 Black Holes with Angular Momentum
146(2)
8.3 Frame-drag
148(2)
8.4 Calculation of the GP-B Predictions
150(15)
8.5 Kerr Space Geodesies
165(14)
8.6 An Interstellar Example
179(4)
9 Cosmology
183(34)
9.1 Robertson--Walker Metric
183(5)
9.2 The Red Shift
188(3)
9.3 Determining Distance
191(5)
9.4 Red Shift Versus Distance Relation
196(3)
9.5 Fluids
199(3)
9.6 Robertson--Walker Einstein Dynamics
202(4)
9.7 The Early Universe
206(3)
9.8 Matter and Dark Energy Domination
209(8)
Bibliography 217(2)
Index 219