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General Relativity: A First Examination [Pehme köide]

(Virginia Tech, Usa)
  • Formaat: Paperback / softback, 192 pages
  • Ilmumisaeg: 05-Aug-2016
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813108479
  • ISBN-13: 9789813108479
Teised raamatud teemal:
  • Formaat: Paperback / softback, 192 pages
  • Ilmumisaeg: 05-Aug-2016
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813108479
  • ISBN-13: 9789813108479
Teised raamatud teemal:
"This manuscript aims to be a textbook for a one semester introduction to General Relativity for advanced undergraduate physics majors and engineers. The book is concise so that all of its material could be covered in the one semester time frame. In addition, the readers are introduced to the guts of the subject quickly without advanced mathematics. Students are daunted by very thick books that they know won't be completely covered. They also are impatient about wading through higher mathematics in a onesemester course. Though concise, the theory development is transparent and the readers are exposed to the possible analytic calculations. The full solutions to some important problems are provided, and the experimental evidence is discussed"--

This manuscript aims to be a textbook for a one semester introduction to General Relativity for advanced undergraduate physics majors and engineers. The book is concise so that all of its material could be covered in the one semester time frame. In addition, the readers are introduced to the guts of the subject quickly without advanced mathematics. Students are daunted by very thick books that they know won't be completely covered. They also are impatient about wading through higher mathematics in a one semester course. Though concise, the theory development is transparent and the readers are exposed to the possible analytic calculations. The full solutions to some important problems are provided, and the experimental evidence is discussed.
Preface vii
Acknowledgments ix
1 Review of Special Relativity
1(14)
1.1 Introduction
1(3)
1.2 Lorentz Transform
4(2)
1.3 Physics Consequences
6(4)
1.4 Spacetime Diagrams
10(5)
2 Vectors and Tensors in Spacetime
15(22)
2.1 Metric Tensor
15(1)
2.2 Vector Transforms
16(2)
2.3 Tensor Transforms
18(1)
2.4 Forming Other Vectors
19(1)
2.5 Twin Problem Revisited
20(2)
2.6 Momentum and Energy
22(1)
2.7 Doppler Shift
23(2)
2.8 Gravity Affects Time
25(1)
2.9 The Pound Rebka Experiment
26(2)
2.10 Global Positioning System
28(3)
2.11 Tensor Equations
31(6)
3 Covariant Differentiation, Equations of Motion
37(14)
3.1 Differentiation of Invariants and Vectors
37(4)
3.2 Differentiation of Tensors
41(1)
3.3 Gravity and the Locally Inertial Frame
42(2)
3.4 Local Flatness Theorem
44(2)
3.5 GR Equations of Motion
46(5)
4 Curvature
51(14)
4.1 Geodesics
51(4)
4.2 Parallel Transport
55(4)
4.3 Curvature Tensors
59(1)
4.4 Ricci Tensor, Bianchi Identity, Einstein Tensor
60(5)
5 Gravity and General Relativity
65(14)
5.1 Review of Newtonian Gravity
65(2)
5.2 Weak Gravity in GR
67(1)
5.3 Gravitational Red Shift
68(2)
5.4 Einstein's Field Equations
70(2)
5.5 Schwarzschild Solution
72(2)
5.6 Conserved Quantities --- Massive Particles
74(5)
6 Solar System Tests of General Relativity
79(16)
6.1 Equations of Motion
79(3)
6.2 Orbit Equations
82(1)
6.3 Light Deflection
83(3)
6.4 Perihelia Advance
86(4)
6.5 Radar Signal Delay
90(5)
7 Black Holes
95(12)
7.1 Static Black Holes
95(4)
7.2 Black Holes With Angular Momentum
99(3)
7.3 An Interstellar Example
102(5)
8 Gravitational Waves
107(32)
8.1 The Weak Gravity Wave Equation
107(3)
8.2 Plane Waves
110(2)
8.3 The Graviton
112(1)
8.4 Gravitational Waves Affect Particles
113(2)
8.5 Wave Equation Solution With Sources
115(3)
8.6 The Energy-Momentum Tensor
118(2)
8.7 Quadrupole Radiation
120(2)
8.8 Gravity Wave Flux and Power
122(7)
8.9 Binary Neutron Star System Radiation
129(10)
9 Cosmology
139(32)
9.1 Robertson-Walker Metric
139(4)
9.2 The Red Shift
143(3)
9.3 Determining Distance
146(5)
9.4 Red Shift Versus Distance Relation
151(4)
9.5 Fluids
155(2)
9.6 Robertson-Walker Einstein Dynamics
157(4)
9.7 The Early Universe
161(4)
9.8 Matter and Dark Energy Domination
165(6)
Bibliography 171(2)
Index 173