The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations (Q1819391): Difference between revisions

The paper is the continuation of author's previous papers [ibid. 105, 337-362 (1986; Zbl 0608.35039), and 106, 587-622 (1986; see the preceding review)] on the global existence of generalized solutions of spherically symmetric Einstein-scalar field equations \(R_{\mu \nu}=8\pi \partial_{\mu}\phi \partial_{\nu}\phi\), in the large. In terms of a retarded time coordinate u and a radial coordinate r, the metric is taken to be of the form \[ ds^ 2=-e^{2\nu} du^ 2-2e^{\nu +\lambda} du dr+r^ 2 d\Sigma^ 2, \] where \(d\Sigma^ 2\) is the metric of the standard 2-sphere. In this paper, the regularity properties of the space- time and the scalar field corresponding to a generalized solution, including the behavior of the generalized solution at null infinity, are studied. The uniqueness theorem is stated and proved in the following form: ''A generalized solution'' having the same data as a classical solution coincides with it in the domain of existence of the latter.''