Preface |
|
v | |
Acknowledgements |
|
vii | |
|
1 Terminology and notation |
|
|
1 | (10) |
|
|
7 | (4) |
Part I |
|
|
2 The elements of General Relativity |
|
|
11 | (16) |
|
2.1 The gravitational field equations: first view |
|
|
12 | (7) |
|
2.2 The strong equivalence principle |
|
|
19 | (5) |
|
2.3 The source of gravity |
|
|
24 | (2) |
|
|
26 | (1) |
|
3 An introductory example: the uniform static field |
|
|
27 | (5) |
|
|
31 | (1) |
|
4 Life in a rotating world |
|
|
32 | (8) |
|
4.1 The canonical form of the stationary metric |
|
|
37 | (1) |
|
4.2 The lessons of the rotating cylinder |
|
|
38 | (1) |
|
|
39 | (1) |
|
5 Linearized General Relativity |
|
|
40 | (16) |
|
5.1 Global Lorentz transformations |
|
|
42 | (2) |
|
5.2 Coordinate transformations and gauge transformations |
|
|
44 | (1) |
|
5.3 The linearized field equations |
|
|
45 | (4) |
|
|
49 | (2) |
|
5.5 Field energy and the gravity of gravity |
|
|
51 | (3) |
|
|
54 | (2) |
|
6 Slow stationary sources |
|
|
56 | (9) |
|
6.1 Gravitational 'Maxwell's equations' |
|
|
56 | (3) |
|
6.2 Lense-Thirring precession |
|
|
59 | (3) |
|
|
62 | (3) |
|
|
65 | (30) |
|
7.1 Identifying and simplifying the plane wave solutions |
|
|
65 | (2) |
|
7.2 The physical impact of a gravitational wave |
|
|
67 | (6) |
|
7.3 Sources of gravitational waves |
|
|
73 | (5) |
|
7.4 Energy flux in gravitational waves |
|
|
78 | (6) |
|
7.5 The detection of gravitational radiation |
|
|
84 | (6) |
|
|
90 | (5) |
Part II |
|
|
|
95 | (14) |
|
|
95 | (4) |
|
|
99 | (4) |
|
8.3 Local flatness and Riemann normal coordinates |
|
|
103 | (3) |
|
8.4 Measuring length, area and volume |
|
|
106 | (2) |
|
|
108 | (1) |
|
|
109 | (12) |
|
9.1 Basis vectors and the inner product |
|
|
110 | (8) |
|
9.2 An example: plane polar coordinates |
|
|
118 | (2) |
|
|
120 | (1) |
|
|
121 | (12) |
|
10.1 Connection coefficients and covariant derivative |
|
|
121 | (7) |
|
10.2 Differentiation along a curve |
|
|
128 | (2) |
|
10.3 Extending the example: plane polar coordinates |
|
|
130 | (1) |
|
|
131 | (2) |
|
|
133 | (11) |
|
11.1 Some physics related to 4-velocity |
|
|
133 | (2) |
|
|
135 | (2) |
|
|
137 | (3) |
|
11.4 Gauss' divergence theorem |
|
|
140 | (2) |
|
|
142 | (2) |
|
|
144 | (16) |
|
12.1 The components of a tensor |
|
|
145 | (3) |
|
12.2 Transformation of Γ and relation to geodesic coordinates |
|
|
148 | (2) |
|
|
150 | (1) |
|
12.4 Covariant derivative of tensors |
|
|
150 | (6) |
|
12.5 Tensors of rank zero |
|
|
156 | (1) |
|
12.6 Tensor density and the Hodge dual |
|
|
157 | (1) |
|
|
158 | (2) |
|
13 Parallel transport and geodesics |
|
|
160 | (18) |
|
|
160 | (6) |
|
13.2 Metric geodesic: most proper time and least distance |
|
|
166 | (2) |
|
|
168 | (1) |
|
13.4 Conservation laws and Killing vectors |
|
|
169 | (1) |
|
13.5 Fermi-Walker transport |
|
|
170 | (2) |
|
13.6 Gravitational redshift |
|
|
172 | (3) |
|
|
175 | (2) |
|
|
177 | (1) |
|
14 Physics in curved spacetime |
|
|
178 | (11) |
|
|
179 | (2) |
|
14.2 Fluid flow and continuous media |
|
|
181 | (4) |
|
14.3 How General Relativity works |
|
|
185 | (2) |
|
14.4 Generally covariant physics |
|
|
187 | (1) |
|
|
188 | (1) |
|
|
189 | (24) |
|
15.1 Quantifying curvature |
|
|
189 | (6) |
|
15.2 Relating Rabcd to parallel transport |
|
|
195 | (5) |
|
|
200 | (5) |
|
|
205 | (2) |
|
15.5 Symmetries of spacetime |
|
|
207 | (4) |
|
|
211 | (2) |
|
16 The Einstein field equation |
|
|
213 | (16) |
|
16.1 Derivation of the field equation |
|
|
213 | (3) |
|
16.2 Stability and energy conditions |
|
|
216 | (1) |
|
16.3 Field equation for a small region |
|
|
217 | (3) |
|
16.4 Motion of matter from the field equation |
|
|
220 | (1) |
|
16.5 The cosmological constant |
|
|
221 | (1) |
|
|
222 | (2) |
|
|
224 | (5) |
Part III |
|
|
17 Schwarzschild-Droste solution |
|
|
229 | (20) |
|
17.1 Obtaining the metric |
|
|
229 | (4) |
|
|
233 | (8) |
|
17.3 Light in Schwarzschild spacetime |
|
|
241 | (5) |
|
|
246 | (1) |
|
|
247 | (2) |
|
18 Further spherically symmetric solutions |
|
|
249 | (11) |
|
18.1 Interior Schwarzschild solution |
|
|
250 | (5) |
|
18.2 Reissner-Nordstrom metric |
|
|
255 | (3) |
|
18.3 de Sitter-Schwarzschild metric |
|
|
258 | (1) |
|
|
258 | (2) |
|
19 Rotating bodies; the Kerr metric |
|
|
260 | (14) |
|
19.1 The general stationary axisymmetric metric |
|
|
260 | (2) |
|
19.2 Stationary limit surface and ergoregion |
|
|
262 | (2) |
|
|
264 | (4) |
|
19.4 Freefall motion in the plane Θ = π/2 |
|
|
268 | (4) |
|
|
272 | (2) |
|
|
274 | (27) |
|
|
274 | (5) |
|
20.2 Null surfaces and event horizons |
|
|
279 | (4) |
|
20.3 The Schwarzschild horizon |
|
|
283 | (2) |
|
20.4 Black hole formation |
|
|
285 | (6) |
|
20.5 Kruskal-Szekeres spacetime |
|
|
291 | (5) |
|
20.6 Astronomical evidence for black holes |
|
|
296 | (3) |
|
|
299 | (2) |
|
21 Black hole thermodynamics |
|
|
301 | (18) |
|
|
301 | (3) |
|
21.2 Area theorem and entropy |
|
|
304 | (2) |
|
21.3 Unruh and Hawking effects |
|
|
306 | (7) |
|
21.4 Laws of black hole mechanics |
|
|
313 | (3) |
|
|
316 | (3) |
Part IV |
|
|
|
319 | (34) |
|
22.1 Observed properties of the universe |
|
|
319 | (11) |
|
22.2 Cosmic time and space |
|
|
330 | (4) |
|
22.3 Friedmann-Lemaitre-Robertson-Walker metric |
|
|
334 | (3) |
|
22.4 Redshift in an expanding space |
|
|
337 | (3) |
|
22.5 Visualizing the evolution of a curved space |
|
|
340 | (7) |
|
22.6 Luminosity distance, angular diameter distance |
|
|
347 | (2) |
|
22.7 The cosmic distance ladder |
|
|
349 | (3) |
|
|
352 | (1) |
|
|
353 | (26) |
|
23.1 The Friedmann equations |
|
|
353 | (4) |
|
23.2 Solving the Friedmann equations |
|
|
357 | (12) |
|
23.3 The physical interpretation of the cosmological constant |
|
|
369 | (1) |
|
23.4 Particle horizon and event horizon |
|
|
370 | (5) |
|
|
375 | (1) |
|
|
376 | (3) |
|
24 The growth of structure |
|
|
379 | (19) |
|
24.1 The structure equations |
|
|
381 | (3) |
|
24.2 Linearized treatment |
|
|
384 | (6) |
|
|
390 | (4) |
|
24.4 Baryon acoustic oscillations |
|
|
394 | (1) |
|
|
395 | (1) |
|
|
396 | (2) |
|
25 Observational cosmology |
|
|
398 | (19) |
|
25.1 Models, statistical and systematic error |
|
|
398 | (2) |
|
25.2 The age of the universe |
|
|
400 | (1) |
|
25.3 Hubble parameter and deceleration parameter |
|
|
401 | (5) |
|
25.4 Baryon acoustic oscillations |
|
|
406 | (3) |
|
25.5 The cosmic microwave background radiation |
|
|
409 | (7) |
|
|
416 | (1) |
|
26 The very early universe |
|
|
417 | (18) |
|
26.1 The horizon and flatness 'problems' |
|
|
419 | (3) |
|
|
422 | (10) |
|
|
432 | (3) |
Part V |
|
|
27 First steps in classical field theory |
|
|
435 | (14) |
|
27.1 Wave equation and Klein-Gordon equation |
|
|
436 | (3) |
|
|
439 | (3) |
|
27.3 Lorentz transformation of spinors |
|
|
442 | (7) |
|
28 Lagrangian mechanics for fields |
|
|
449 | (11) |
|
|
452 | (1) |
|
28.2 Conserved quantities and Noether's theorem |
|
|
453 | (3) |
|
|
456 | (1) |
|
28.4 The Einstein-Hilbert action |
|
|
457 | (3) |
|
|
460 | (3) |
Appendix A Kepler orbits for binary system |
|
463 | (3) |
Appendix B The 2-sphere and the 3-sphere |
|
466 | (5) |
|
|
466 | (2) |
|
|
468 | (2) |
|
|
470 | (1) |
Appendix C Differential operators as vectors |
|
471 | (3) |
Appendix D General equations of the linearized theory |
|
474 | (4) |
Appendix E Gravitational energy |
|
478 | (3) |
Appendix F Causality and the Cauchy problem in General Relativity |
|
481 | (4) |
References |
|
485 | (4) |
Index |
|
489 | |