A First Course in General RelativityGeneral relativity has become one of the central pillars of theoretical physics, with important applications in both astrophysics and highenergy particle physics, and no modern theoretical physicist's education should be regarded as complete without some study of the subject. This textbook, based on the author's own undergraduate teaching, develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth. It reinforces this understanding by making a detailed study of the theory's most important applications  neutron stars, black holes, gravitational waves, and cosmology  using the most uptodate astronomical developments. The book is suitable for a oneyear course for beginning graduate students or for undergraduates in physics who have studied special relativity, vector calculus, and electrostatics. Graduate students should be able to use the book selectively for halfyear courses. 
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Review: A First Course in General Relativity
User Review  Ian Durham  GoodreadsThe best introductory text on the subject that exists. One of the best texts I've ever read. Read full review
Review: A First Course in General Relativity
User Review  Matt  GoodreadsWell written from a mathematics viewpoint. Not 100% application but still a good text. Chapter 6 on Curved Manifolds was my favorite. Read full review
Contents
II  1 
III  4 
IV  5 
V  6 
VI  7 
VII  10 
VIII  15 
IX  18 
LIV  151 
LV  154 
LVI  160 
LVII  163 
LVIII  167 
LIX  173 
LX  175 
LXI  176 
X  24 
XI  25 
XII  26 
XIII  27 
XIV  28 
XV  30 
XVI  36 
XVII  39 
XVIII  44 
XIX  45 
XX  47 
XXI  50 
XXII  52 
XXIII  53 
XXIV  54 
XXV  60 
XXVI  61 
XXVII  62 
XXVIII  71 
XXIX  73 
XXX  77 
XXXI  78 
XXXII  80 
XXXIII  81 
XXXV  89 
XXXVI  90 
XXXVII  94 
XXXVIII  97 
XXXIX  99 
XL  106 
XLI  110 
XLII  111 
XLIII  112 
XLIV  113 
XLV  118 
XLVI  126 
XLVII  133 
XLVIII  140 
XLIX  143 
L  144 
LI  147 
LII  148 
LXIII  182 
LXIV  185 
LXV  188 
LXVI  189 
LXVII  191 
LXIX  195 
LXX  199 
LXXI  200 
LXXII  205 
LXXIII  208 
LXXIV  209 
LXXV  214 
LXXVI  221 
LXXVII  226 
LXXVIII  234 
LXXIX  242 
LXXX  243 
LXXXI  251 
LXXXII  253 
LXXXIII  255 
LXXXIV  257 
LXXXV  258 
LXXXVI  261 
LXXXVII  264 
LXXXVIII  270 
LXXXIX  271 
XC  275 
XCI  288 
XCII  294 
XCIII  305 
XCIV  310 
XCV  311 
XCVI  318 
XCVII  322 
XCVIII  329 
XCIX  334 
C  338 
CII  342 
CIII  346 
359  
367  
Common terms and phrases
acceleration algebra angular momentum arbitrary axis basis vectors black hole calculate called Christoffel symbols clock components conservation const constant coordinate system covariant derivative curvature curve defined definition Derive Eq differential direction discussion distance Einstein Einstein's equations energy Euclidean space Exer flat fluid element flux fourmomentum fourvelocity frame G freely falling function galaxies gauge geodesic geometry gives gradient gravitational field gravitational waves horizon hyperbolae implies independent inertial frame integral inverse line element linear Lorentz transformation manifold matrix MCRF measured metric tensor Misner Newtonian notation null number density observer oneform orbit orthogonal oscillator parameter particle photon physical plane polar coordinates radiation radius real number redshift relative relativistic rest mass rotation scalar Schwarzschild Schwarzschild metric Show sin2 solution spacetime diagram spatial speed sphere star stressenergy tensor surface tangent theory timelike trajectory unit vanish velocity world line zero
Popular passages
Page 359  The theory of separability of the HamiltonJacobi equation and its applications to general relativity.