Scalarization of horizonless reflecting stars: Neutral scalar fields non-minimally coupled to Maxwell fields

Abstract

We analyze condensation behaviors of neutral scalar fields outside horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was known that minimally coupled neutral scalar fields cannot exist outside horizonless reflecting stars. In this work, we consider non-minimal couplings between scalar fields and Maxwell fields, which is included to aim to trigger formations of scalar hairs. We analytically demonstrate that there is no hair theorem for small coupling parameters below a bound. For large coupling parameters above the bound, we numerically obtain regular scalar hairy configurations supported by horizonless reflecting stars.

Scalarized Einstein–Maxwell-scalar black holes in anti-de Sitter spacetime

“…To better understand the dynamical evolution into scalarized black holes, a similar, but technically simpler, class of models, i.e., Einstein-Maxwell-scalar (EMS) models with non-minimal couplings between the scalar and Maxwell fields, has been put forward in [24], where fully non-linear numerical evolutions of spontaneous scalarization were presented. Subsequently, further studies of spontaneous scalarization in the EMS models were discussed in the context of various nonminimal coupling functions [25,26], dyons including magnetic charges [27], axionic-type couplings [28], massive and self-interacting scalar fields [29,30], horizonless reflecting stars [31], stability analysis of scalarized black holes [32][33][34][35][36], higher dimensional scalar-tensor models [37], quasinormal modes of scalarized black holes [38,39], two U(1) fields [40], quasi-topological electromagnetism [41], topology and spacetime structure influences [42] and the Einstein-Born-Infeld-scalar theory [43]. Besides the above asymptotically flat scalarized black holes, spontaneous scalarization was also discussed in the EMS model with a positive cosmological constant [44].…”

Charged reflecting shells supporting non-minimally coupled massless scalar field configurations

“…In particular, using analytical techniques, we have derived the remarkably compact dimensionless formula [see Eq. ( 15 The analytically derived resonance spectrum (22) implies that, for given values {R s , Q} of the physical parameters of the central supporting shell, the dimensionless coupling parameter α of the composed charged-shell-nonminimallycoupled-massless-scalar-field theory is an increasing function of the resonance parameter n. In particular, in the regime n l of large overtone numbers, one may use the asymptotic relation (see Eqs. 9.5.12 of [24]) j l+ 1 2 ,n = π [n + of the resonance spectrum.…”

“…In addition, the resonance spectrum (22) implies that the dimensionless coupling parameter α of the composed charged-shell-nonminimally-coupled-massless-scalar-field configurations is an increasing function of the angular harmonic index l. In particular, in the regime l n of large angular harmonic indices, one may use the asymptotic relation (see Eq. 9.5.14 of [24]) j l+ 1 2 ,n = (l + 1 2 )[1 + O(l −2/3 )] for the zeros of the Bessel function, which yields the asymptotic large-l behavior (Note that ( 22), ( 23), and ( 24) are dimensionless expressions.…”

“…In particular, using analytical techniques (The case of massive non-minimally coupled scalar fields was studied numerically in the interesting work [22]. In the present paper we shall explicitly prove that the case of massless non-minimally coupled scalar fields can be studied analytically), we shall explicitly prove below that, for a spherically symmetric compact reflecting shell of electric charge Q, there exists an infinitely large discrete resonance spec-trum {R s (Q, α; n)} n=∞ n=1 of shell radii that can support nonminimally coupled massless scalar field configurations [here the physical parameter α is the dimensionless coupling parameter between the supported scalar field and the electromagnetic field of the central charged shell, see Eq.…”

Scalarized Einstein–Maxwell-scalar black holes in a cavity

“…In [17], the analytical technique is applied to solve the Klein-Gordon wave equation for the non-minimally coupled linearized scalar fields in the spacetimes of near-extremal supporting black holes. Furthermore, spontaneous scalarization in the EMS models was discussed in context of coupling functions beyond the exponential coupling [18,19], dyons including magnetic charges [20], axionic-type couplings [21], massive and self-interacting scalar fields [22,23], horizonless reflecting stars [24], linear stability of scalarized black holes [25][26][27], higher dimensional scenario [28], quasinormal modes of scalarized black holes [29,30], two U(1) fields [31] and quasi-topological electromagnetism [32]. Moreover, the EMS models with a cosmological constant are considered in [33,34].…”