Static spherically symmetric black holes with scalar field

TL;DR

This paper analyzes static spherically symmetric black holes and particle-like solutions with scalar fields, establishing conditions for their properties, asymptotics, and potentials, including no-hair theorems and horizon characteristics.

Contribution

It introduces a unified framework using a single function { ho} to characterize solutions and generalizes no-hair theorems to AdS spacetimes, exploring various potential classes.

Findings

Positive ADM mass for nontrivial scalar fields

Horizon radius cannot exceed twice the mass

Multiple classes of solutions with different potentials

Abstract

Static spherically symmetric black holes and particle like solutions with self interacting minimally coupled scalar field {\phi} are analyzed. They are asymptotically flat or anti-de Sitter (AdS). We express them in terms of a single function {\rho} which undergoes simple conditions. If {\phi} 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 {\rho} at singularity determine properties of admissible potentials V({\phi}) as regularity, boundedness and behaviour for maximal values of {\phi}. Several classes of solutions with singular or nonsingular potentials are obtained. Their examples are presented in a form of plots.