mrsmeath said:
I've got a coursework to get done on the detection methods of black holes. So far I'm aware of gravitational lensing, x-ray detection and the accretion discs, and have just about finished my section on gravitational lensing. I'm wondering though if anyone has some (reliable) links or good insight into the detailed theories and formulae (no matter how complicated) behind the last two.
It's not a full answer, but check out
this thread if you haven't already.
Really, you're asking a big question, as black holes play a huge role in modern astrophysics...which is funny, because we're not 100% sure they exist! What we do know is that there are several places in the universe in which there's a
lot of mass compacted into a very small space (by astrophysical standards).
Here is a nice link on stellar mass black holes. The basic idea is that we observe systems of binary stars and determine the parameters of the system (masses, velocities, radii, etc.) based on various measurements. If we determine that one component of the system is very massive (greater than three times that of the sun) but isn't giving off any light, we assume that it's a black hole. There are various physical reasons for that assumption that I can go into in more detail on if you like.
Another place we see black holes is at the centers of galaxies and we call these supermassive black holes (SMBHs). Most of the ones we've seen so far are greater than a million times the mass of our sun, though they can get up to a billion solar masses. The way we measure these masses is similar; that is, we look at the motions of stars near the black hole and use Newtonian gravity to infer a mass for the object.
We assume that these are the same objects that produce quasars (or, more generally, active galactic nucleii), partially because they're in the same location (the centers of galaxies) and partially because we can't think of anything else that could steadily produce that much light. To infer the masses of these objects, we can't use dynamical measurements (the quasars shine so brightly that the nearby stars are difficult to see). Rather, we
infer a mass based on the luminosity. I suggest looking into something called the "Eddington Luminosity", because it gives a rough limit for the luminosity of an object of a given mass. When an object exceeds this luminosity limit, the radiation pressure becomes so strong that the object has a tendency to blow itself apart. In the case of black holes, it's not the black hole itself that would be blown apart, but rather the material accreting around it.
EDIT: Oh, and does anyone know of a method which can calculate the Schwarzschild radius of something without knowing its mass? sounds unlikely to me from what i know about it but maybe I am wrong...
Well, the Schwarzschild radius is defined by:
r_g = \frac{2GM}{c^2}
so it doesn't make sense to calculate it without a mass (or a set of equivalent parameters).
I've got till thursday morning so if anyone else can plant a few more seeds of wisdom, id appreciate anything u can throw me (i like working till the last minute) 
