Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large

In this paper we study the global initial value problem for the spherically symmetric Einstein-scalar field equations in the large. We introduce the concept of a generalized solution of our problem, and, taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, without any restriction on the size of the initial data, the global, in retarded time, existence of generalized solutions.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University