General relativity is a beautiful scheme for describing the gravitational Feld and the
equations it obeys. Nowadays this theory is often used as a prototype for other, more
intricate constructions to describe forces between elementary particles or other branches of
fundamental physics. This is why in an introduction to general relativity it is of importance
to separate as clearly as possible the various ingredients that together give shape to this
After explaining the physical motivations we Frst introduce curved coordinates, then
add to this the notion of an aﬃne connection Feld and only as a later step add to that the
metric Feld. One then sees clearly how space and time get more and more structure, until
Fnally all we have to do is deduce Einstein’s Feld equations.
As for applications of the theory, the usual ones such as the gravitational red shift,
the Schwarzschild metric, the perihelion shift and light deﬂection are pretty standard.
They can be found in the cited literature if one wants any further details. I do pay some
extra attention to an application that may well become important in the near future:
gravitational radiation. The derivations given are often tedious, but they can be produced
rather elegantly using standard Lagrangian methods from Feld theory, which is what will
be demonstrated in these notes.
C.W. Misner, K.S. Thorne and J.A. Wheeler, “Gravitation”, W.H. ±reeman and Comp.,
San ±rancisco 1973, ISBN 0-7167-0344-0.
R. Adler, M. Bazin, M. Schi²er, “Introduction to General Relativity”, Mc.Graw-Hill 1965.
R. M. Wald, “General Relativity”, Univ. of Chicago Press 1984.
P.A.M. Dirac, “General Theory of Relativity”, Wiley Interscience 1975.
S. Weinberg, “Gravitation and Cosmology: Principles and Applications of the General
Theory of Relativity”, J. Wiley & Sons. year ???
S.W. Hawking, G.±.R. Ellis, “The large scale structure of space-time”, Cambridge Univ.
S. Chandrasekhar, “The Mathematical Theory of Black Holes”, Clarendon Press, Oxford
Univ. Press, 1983
Dr. A.D. ±okker, “Relativiteitstheorie”, P. Noordho², Groningen, 1929.