Static self-gravitating elastic bodies in Einstein gravity
  We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations without symmetries. 
Lars Andersson (UM and AEI), Robert Beig (Vienna), Bernd Schmidt (AEI)