Preface |
|
vii | |
Acknowledgments |
|
ix | |
|
1 Review of Special Relativity |
|
|
1 | (16) |
|
|
1 | (4) |
|
|
5 | (2) |
|
|
7 | (4) |
|
|
11 | (6) |
|
2 Vectors and Tensors in Spacetime |
|
|
17 | (24) |
|
|
17 | (1) |
|
|
18 | (3) |
|
|
21 | (1) |
|
2.4 Forming Other Vectors |
|
|
22 | (1) |
|
2.5 Twin Problem Revisited |
|
|
23 | (3) |
|
|
26 | (1) |
|
|
26 | (2) |
|
|
28 | (1) |
|
2.9 The Pound--Rebka Experiment |
|
|
29 | (2) |
|
2.10 Global Positioning System |
|
|
31 | (4) |
|
|
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) |
|
|
55 | (14) |
|
|
55 | (4) |
|
|
59 | (4) |
|
|
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) |
|
|
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) |
|
|
91 | (3) |
|
|
94 | (1) |
|
|
95 | (3) |
|
|
98 | (4) |
|
|
102 | (5) |
|
|
107 | (34) |
|
7.1 The Weak Gravity Wave Equation |
|
|
107 | (3) |
|
|
110 | (2) |
|
|
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) |
|
|
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) |
|
|
141 | (5) |
|
8.2 Black Holes with Angular Momentum |
|
|
146 | (2) |
|
|
148 | (2) |
|
8.4 Calculation of the GP-B Predictions |
|
|
150 | (15) |
|
|
165 | (14) |
|
8.6 An Interstellar Example |
|
|
179 | (4) |
|
|
183 | (34) |
|
9.1 Robertson-Walker Metric |
|
|
183 | (5) |
|
|
188 | (3) |
|
|
191 | (5) |
|
9.4 Red Shift Versus Distance Relation |
|
|
196 | (3) |
|
|
199 | (3) |
|
9.6 Robertson-Walker Einstein Dynamics |
|
|
202 | (4) |
|
|
206 | (3) |
|
9.8 Matter and Dark Energy Domination |
|
|
209 | (8) |
Bibliography |
|
217 | (2) |
Index |
|
219 | |