Selfgravitating nonlinear scalar fields

Abstract

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 $H_1\cap H_{1,4}$ 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.

30 pages

Cited by in corpus (5)

• Naked singularities and Seifert's conjecture
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Spherical scalar waves and gravity - red shift and backscattering
• On the Bach and Einstein equations in presence of a field
• Collapse of a self-similar cylindrical scalar field with non-minimal coupling II: strong cosmic censorship