On H. Friedrich's formulation of Einstein'equations with fluid sources
  We establish a variant, which has the advantage of introducing only physical characteristics, of the symmetric quasi linear first order system given by H.\ Friedrich for the evolution equations of gravitating fluid bodies in General Relativity which can be important to solve realistic problems. We explicit the conditions under which the system is hyperbolic and admits a well posed Cauchy problem. 
Yvonne Choquet-Bruhat and James W. York