Intrinsic formulation of the Cauchy problem in general relativity

In the wide spread Literature there are many approaches to the Cauchy problem in General relativity, both in general and harmonic coordinates, for empty space- time or with energetic sources; either local or semi-global, asymptotically minkowskian, and global solutions are considered. A new approach is given, considering a general and intrinsic formulation of the evolution problem for a space-time corresponding to a non-polar continuum. Einstein's equations are coupled with the heat equations recently proposed as the more natural extension of the classic situation. The general model proposed here, assumes that the proper constitutive equations of the continuum, that is the explicit laws for both the mechanical stress Xik and internal energy ε are given. More precisely a 3- dimensional formulation is given for the evolution problem of both the material continuum and associated space-time