SELF-GRAVITATING NONLINEAR SCALAR FIELDS

We investigate the Cauchy problem for the Einstein - scalar field equa tions in asymptotically flat spherically symmetric spacetimes, in the standard 1+3 formulation. We prove the local existence and uniqueness of solutions for initial data given on a space-like hypersurface in th e Sobolev H-1 boolean AND H-1,H-4 space. Solutions exist globally if a central (integral) singularity does not form and/or outside an outgoi ng null hypersurface. An explicit example demonstrates that there exis ts a local evolution with a naked initial curvature singularity at the symmetry centre. (C) 1997 American Institute of Physics.