Selfgravitating nonlinear scalar fields
نویسنده
چکیده
We investigate the Cauchy problem for the Einstein scalar field equations 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 the Sobolev H1∩H1,4 space. Solutions exist globally if a central (integral) singularity does not form and/or outside an outgoing null hypersurface. An explicit example demonstrates that there exists a local evolution with a naked initial curvature singularity at the symmetry centre.
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