Scalar hairy black holes and solitons in asymptotically flat spacetimes

Abstract

A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\phi)$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations for the minimal coupling case, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture. For the nonminimal coupling case, the stability will be analyzed in a forthcoming paper.Comment: 7 pages, 10 postscript figures, file tex, new postscript figs. and references added, stability analysis revisite

(Higgs) vacuum decay during inflation

“…For the time being V and f are generic functions of the scalar field h. The action in eq. (2.1) is the most general action for the metric g µν and h up to two-derivative terms: an extra generic function Z(h) multiplying the kinetic term of the scalar field can be removed by redefining h. The classical equations of motion for gravity and for h are [25] …”

Dynamical evolution of unstable self-gravitating scalar solitons

“…It is also important to mention that, having fixed the parameters of the potential, this static solution is unique, as opposed to the case of the corresponding hairy black holes where the family of static solutions is parametrized by the horizon radius [1].…”

“…[1], plus/minus a small Gaussian perturbation in Π. Strictly speaking, pure static initial conditions would not result in non-trivial evolution.…”

Scalar hairy black holes and scalarons in the isolated horizons formalism

“…Recently, numerical evidence for the existence of asymptotically flat and static spherically symmetric solutions representing scalar hairy black holes (SHBH) and scalar solitons (scalarons; hereafter SS) have been found in theories represented by the action (4) and with a scalar potential non-positive-semidefinite [12] given by the asymmetric potential,…”

“…As in Ref. [12], we shall take the specific values η 1 = 0.5, η 2 = 0.1 and a = 0; all the quantities (e.g., M ADM and r ∆ ) have been rescaled as appropriate using 1/ √ λ as a length-unit. The first consequence coming from the IH formalism is that the horizon mass associated to the SHBH takes the form 1 ,…”