Spherically symmetric false vacuum: No-go theorems and global structure - art. no. 064013

I enumerate all possible types of spacetime causal structures that can appe ar in static. spherically symmetric configurations of a self-gravitating, r eal, nonlinear, minimally coupled scalar field cp in general relativity, wi th an arbitrary potential V(phi), not necessarily positive definite. It is shown that a variable scalar field adds nothing to the list of possible str uctures with a constant phi field, namely, Minkowski [or anti-de Sitter (Ad S)], Schwarzschild, de Sitter, and Schwarzschild-de Sitter structures. It f ollows in particular that whatever V(phi) is, this theory does not admit re gular black holes with flat or AdS asymptotics. It is concluded that the on ly possible globally regular, asymptotically flat solutions are solitons wi th a regular center, without horizons and with at least partly negative pot entials V(phi). Extension of the results to more general field models is di scussed.