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

Hod, Shahar

doi:10.1140/epjc/s10052-020-7981-z

Cited by 4 publications

(1 citation statement)

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“…For instance, if the scalar field nonminimally couples to the Maxwell (rather than a curvature) invariant F µν F µν , with F µν being the electromagnetic field strength, charged black holes can scalarize in Einstein-Maxwell-scalar models [46][47][48][49][50][51][52][53][54][55][56][57], wherein both the scalar and electromagnetic fields minimally couple to Einstein's gravity (see also [58,59] for scalar field couplings in nonlinear electrodynamics). Additionally, even in the absence of gravity, a nonminimal coupling of the scalar field to Maxwell's electromagnetism, f (φ)F µν F µν , where f (φ) is a regular function of φ, may allow scalarization of a charged object, such as a conducting sphere [46] (see also [60]). This occurs in Maxwell-scalar (Ms) models on Minkowski spacetime, which therefore provide one of the simplest arenas to study the spontaneous scalarization phenomenon.…”

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confidence: 99%

Spontaneous scalarization of a conducting sphere in Maxwell-scalar models

Herdeiro,

Ikeda,

Minamitsuji

et al. 2020

Preprint

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We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwell-scalar models in flat spacetime, wherein the scalar field φ is nonminimally coupled to the Maxwell electrodynamics. This setup serves as a toy model for the spontaneous scalarization of charged (vacuum) black holes in Einstein-Maxwell-scalar (generalized scalar-tensor) models. In the Maxwell-scalar case, unlike the black hole cases, closed-form solutions exist for the scalarized configurations. We compute these configurations for three illustrations of nonminimal couplings: one that exactly linearizes the scalar field equation, and the remaining two that produce nonlinear continuations of the first one. We show that the former model leads to a runaway behaviour in regions of the parameter space and neither the Coulomb nor the scalarized solutions are stable in the model; but the latter models can heal this behaviour producing stable scalarized solutions that are dynamically preferred over the Coulomb one. This parallels reports on black hole scalarization in the extended-scalar-Gauss-Bonnet models. Moreover, we analyse the impact of the choice of the boundary conditions on the scalarization phenomenon. Dirichlet and Neumann boundary conditions accommodate both (linearly) stable and unstable parameter space regions, for the scalar-free conducting sphere; but radiative boundary conditions always yield an unstable scalar-free solution and preference for scalarization. Finally, we perform numerical evolution of the full Maxwell-scalar system, following dynamically the scalarization process. They confirm the linear stability analysis and reveal that the scalarization phenomenon can occur in qualitatively distinct ways. CONTENTS I. Introduction II. Maxwell-scalar (Ms) models A. Action and field equations B. The Coulomb solution embedded in Ms models and its stability III. The linear model A. The scalarized solution B. Instability of the scalarized charged conductor in the linear model IV. Nonlinear models A. The inverse quartic polynomial model B. The inverse cosine coupling C. Stability of the scalarized charged conductor in the nonlinear models V. Time evolutions A. Numerical results 1. Inverse quartic polynomial model 2. Inverse cosine model

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