Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large (Q1819390)

This is a continuation of a previous work of the author [ibid. 105, 337- 362 (1986; Zbl 0608.35039)]. The global initial value problem is studied for the spherically symmetric Einstein-scalar field equations for large initial data on a future light cone. In such a case the global solution may not exist in the classical sense. Therefore a concept of a generalized solution is introduced (Definition 1). The main result (Theorem 1) is that the Einstein-scalar field equations possess at least one generalized solution.