Download Introduction to General Relativity (lecture notes)

General relativity is a beautiful scheme for describing the gravitational field 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 paradigm. After explaining the physical motivations we first introduce curved coordinates, then add to this the notion of an affine connection field and only as a later step add to that the metric field. One then sees clearly how space and time get more and more structure, until finally all we have to do is deduce Einstein’s field 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. In this new version of my lecture notes, mainly chapter 14 was revised, partly due to the recent claims that the effects of a non-vanishing cosmological constant have been detected, but also because I found that the treatment could be adapted more to standard literature on cosmology and at the same time the exposition could be improved. Finally, I do pay 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 field theory, which is what will be demonstrated. When teaching this material, I found that this last chapter is still a bit too technical for an elementary course, but I leave it there anyway, just because it is omitted from introductory text books a bit too often.


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