Essential Relativity: Special, General, and CosmologicalIn retrospect, the first edition of this book now seems like a mere sketch for a book. The present version is, if not the final product, at least a closer approximation to it. The table of contents may show little change. But that is simply because the original organization of the material has been found satisfactory. Also the basic purpose of the book remains the same, and that is to make relativity come alive conceptually. I have always felt much sym pathy with Richard Courant's maxim (as reported and exemplified by Pascual Jordan) that, ideally, proofs should be reached by comprehension rather than computation. Where computations are necessary, I have tried to make them as transparent as possible, so as not to hinder the progress of comprehension. Among the more obvious changes, this edition contains a new section on Kruskal space, another on the plane gravitational wave, and a third on linearized general relativity; it also contains many new exercises, and two appendices: one listing the curvature components for the diagonal metric (in a little more generality than the old" Dingle formulas "), and one syn thesizing Maxwell's theory in tensor form. But the most significant changes and additions have occurred throughout the text. Many sections have been completely rewritten, many arguments tightened, many "asides" added, and, of course, recent developments taken into account. |
Contents
I | 1 |
II | 2 |
III | 3 |
IV | 4 |
VII | 5 |
IX | 6 |
XI | 7 |
XII | 8 |
LIV | 84 |
LV | 86 |
LVI | 87 |
LVII | 88 |
LVIII | 90 |
LIX | 91 |
LX | 93 |
LXI | 96 |
XIII | 9 |
XIV | 10 |
XVI | 11 |
XVII | 14 |
XVIII | 15 |
XIX | 17 |
XX | 19 |
XXI | 20 |
XXII | 23 |
XXIII | 25 |
XXIV | 26 |
XXV | 28 |
XXVI | 29 |
XXVII | 31 |
XXVIII | 33 |
XXIX | 37 |
XXX | 38 |
XXXI | 40 |
XXXIII | 41 |
XXXIV | 43 |
XXXV | 45 |
XXXVI | 47 |
XXXVII | 49 |
XXXVIII | 51 |
XXXIX | 54 |
XL | 55 |
XLI | 57 |
XLII | 61 |
XLIII | 63 |
XLIV | 66 |
XLV | 68 |
XLVI | 70 |
XLVII | 72 |
XLVIII | 75 |
XLIX | 76 |
L | 77 |
LI | 79 |
LII | 81 |
LXII | 100 |
LXIV | 102 |
LXV | 105 |
LXVI | 108 |
LXVII | 110 |
LXVIII | 114 |
LXIX | 117 |
LXX | 119 |
LXXI | 122 |
LXXII | 126 |
LXXIII | 133 |
LXXIV | 136 |
LXXV | 143 |
LXXVI | 149 |
LXXVII | 156 |
LXXVIII | 164 |
LXXIX | 166 |
LXXX | 174 |
LXXXI | 178 |
LXXXII | 183 |
LXXXIII | 188 |
LXXXIV | 193 |
LXXXV | 199 |
LXXXVI | 201 |
LXXXVII | 204 |
LXXXVIII | 207 |
LXXXIX | 212 |
XC | 218 |
XCI | 223 |
XCII | 226 |
XCIII | 230 |
XCIV | 238 |
XCV | 242 |
XCVI | 245 |
XCVII | 247 |
XCVIII | 253 |
| 277 | |
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Common terms and phrases
acceleration angle arbitrary assume axes axis clock collision components consider constant coordinate system corresponding cosmic cosmology curvature curved defined density derivatives diagram differential dilation direction distance do² Doppler Doppler effect ds² dx² Einstein energy equivalent ether Euclidean example field equations Figure finite force formula four-acceleration four-tensors four-vector four-velocity galaxies Galilean transformation geodesic geometry given gravitational field Hence horizon implies inertial frames infinite invariant isotropic length contraction light signal linear Lorentz Lorentz transformations Mach's principle Maxwell's theory metric Minkowski Minkowski space momentum motion moving Newton's theory Newtonian observer orbit origin p₁ particle horizon photon physics plane Poisson's equation prove radial radius relativistic rest frame rest mass result rocket rotation satisfy scalar Schwarzschild Schwarzschild metric Section solution spacetime spatial special relativity sphere static surface symmetry tensor timelike transformation universe vector velocity wave worldlines zero μν