Numerical integration of exact time-dependent Einstein equations with axial symmetry. I

In the present Part I the complete system of exact equations describing a nonstrationary state of an axially symmetric relativistic object consisting of a perfect fluid is reduced to the form suitable for the numerical integration by a computer. it is assumed that all the thermodynamic processes are adiabatic and no nuclear energy is being released, but no restriction is imposed on the analytically expressed equation of state. By the method it is possible to compute the initial data and the time evolution of the interior and exterior field generated either by a single rotating and contracting (or expanding) body, or by two neutron stars before and during their head-on collision. In Part II the method of the numerical integration will be described, its efficiency discussed, and a few examples of integration exhibited.