Static spherically symmetric black holes with scalar field
arXiv:1112.2687 · doi:10.1007/s10714-013-1645-3
Abstract
Static spherically symmetric black holes and particle like solutions with self interacting minimally coupled scalar field ϕ are analyzed. They are asymptotically flat or anti-de Sitter (AdS). We express them in terms of a single function ρ which undergoes simple conditions. If ϕ is nontrivial the ADM mass M has to be positive. No-hair theorems are generalized to the AdS asymptotic. For both asymptotics the Killing horizon is nondegenerate and its radius cannot be bigger than 2M. Derivatives of ρ at singularity determine properties of admissible potentials V(ϕ) as regularity, boundedness and behaviour for maximal values of ϕ. Several classes of solutions with singular or nonsingular potentials are obtained. Their examples are presented in a form of plots.
18 pages, 1 figure