It has found application. The main problem is that Einstein's equations have no type due to the large symmetry group (the whole diffeomorphism group). So First one has to fix a gauge; this is done by fixing a space like hypersurface $\Sigma$. Then the initial conditions are a Riemannian metric on $\Sigma$ and a second funcdamental form along $\Sigma$. It is one of the great advances in nonlinear PDE-theory that then there exists a solution and it is unique and it is smooth, if all initial data are small and smooth. This was proved by Christodoulou and Klainerman. See, e.g.,

- MR1946854 (2004f:58036) Reviewed 
Klainerman, Sergiu(1-PRIN); Nicolò, Francesco(I-ROME2M)
The evolution problem in general relativity. 
Progress in Mathematical Physics, 25. Birkhäuser Boston, Inc., Boston, MA, 2003. xiv+385 pp. ISBN: 0-8176-4254-4 

for an account of this.