Schwarzschild metric: motivations and applications in physics I have a mathematical background and I have just derived the expression of the Schwarzschild metric. Now I was wondering what were the motivations and applications in physics of this metric. Any info would be welcome!
 A: The Schwarzschild metric describes the geometry of the spacetime containing a time independant spherically symmetric mass and nothing else. In other words the spacetime has to have existed unchanged for an infinite time and continue to exist unchanged for an infinite time, and there must be nothing else in the universe. Obviously there is no object in the real universe that is exactly described by the Schwarzschild metric (which has led the loonier end of the physics fringe to claim that black holes don't exist).
However we expect the Schwarzschild metric to be an excellent approximation for spacetime geometry near the sorts of astronomical objects we see around us, like stars and planets as well as (of course) black holes. So for example we can use the Schwarzschild metric to calculate the corrections needed to the clocks on GPS satellites, without worrying that the spacetime geometry in and around the Solar System is a lot more complicated that the Schwarzschild metric describes.
As for specific applications, there must be hundreds of them. Top of the list would be the sorts of applications Stan mentions in his answer.
A: By "derived the Schwarzschild metric" I assume you mean calculating the exterior solution of the form 
$$ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 +r^2\Omega^2$$
Applications:


*

*Describing deflection of light by the sun 

*Precession of the perihelia of the orbits of the inner planets 

*Schwarzschild singularity and blackholes 


You can find info on these in Wald's General Relativity or Weinberg's Gravitation and Cosmology. 
