The idea of this chapter is to go into more detail on a few selected topics in relativity, concentrating on those that are of the most direct interest to the astrophysicist: fluid mechanics, weak fields and orbits therein, gravitational radiation and black holes. A word of warning: so far, all equations have been explicitly dimensional, and contain the correct powers of c; from now on, this will not always be the case. It is common in the literature on relativity to simplify formulae by choosing units where c = 1. Since this can be confusing for the beginner, c will be retained where it does not make the algebra too cumbersome. However, sometimes it will disappear from a derivation temporarily. This should encourage the good habit of always being aware of the dimensional balance of any given equation.

Relativistic fluid mechanics

One of the attractive features of relativity is the economical form that many of its fundamental equations can take. The price paid for this is that the quantities of interest are not always immediately available; the process of ‘unpacking’ some of these expressions can become rather painful and reveal considerable buried complexity. It is worth illustrating this with the example of fluid mechanics, not just for its own sake, but because we will end up with some results that are rather useful in astrophysics and cosmology.