Numerical integration of axially symmetric systems

Using ADM formalism, the authors have calculated the general relativistic collapse of the pressureless matter. The basic flow of the numerical calculation is as follows: determine the initial values of the 3-space metric by solving the constraint equations for an arbitrary baryon density distribution; determine the lapse function and the shift vector to fix the coordinate system; determine space-time geometry and matter distribution at t=t+dt by solving the evolution equations of metric and hydrodynamics equations; and estimate the accuracy of the constraint equations at t=t+dt. The authors return to the second stage and repeat the process until a black hole is formed. (Auth.)