Abstract
We consider an augmented Einstein-Maxwell-scalar model including an axionic-type coupling between the scalar and electromagnetic field. We study dyonic black hole solutions in this model. For the canonical axionic coupling emerging from high energy physics, all charged black holes have axion hair. We present their domain of existence and investigate some physical properties. For other axionic-type couplings, two classes of black hole solutions may coexist in the model: scalar-free Reissner-Nordstr\"om black holes and scalarized black holes. We show that in some region of the parameter space the scalar-free solutions are unstable. Then, there is nonuniqueness since new scalarized black hole solutions with the same global charges, which are entropically preferred over the scalar-free solutions and, moreover, emerge dynamically from the instability of the former, also exist.
Highlights
Three types of bosonic fields, each consistent on its own as a classical relativistic field theory, are used in the physical description of nature: spin-0, -1, and -2 fields
Scaling arguments, initiated by the work of Derrick [38], are a powerful tool to establish no-go theorems for solitonic solutions and no-hair theorems for black hole (BH) solutions [15] as well as to provide a physical relation that must be obeyed by solutions of a given model
This paper considers an augmented EMS sclar model and its BH solutions, in particular in the context of the spontaneous scalarization of charged BHs
Summary
Three types of bosonic fields, each consistent on its own as a classical relativistic field theory, are used in the physical description of nature: spin-0, -1, and -2 fields. We shall illustrate them in the augmented EMS models with a particular choice of nonminimal coupling that allows for the spontaneous scalarization of the RN BH. Spherical symmetry requires the scalar field φðrÞ to have a radial dependence only, and an electromagnetic 4-potential ansatz of the following type, which allows a possible magnetic charge P,. Q r þ ð2:12Þ which introduce three new parameters: the scalar charge Qs, the electrostatic potential difference between the horizon and infinity Φe, and the Arnowitt-Deser-Misner (ADM) mass M From these asymptotic expansions, one collects a set of eight independent parameters, ðrH; Q; P; φ0; δ0; Qs; Φe; MÞ. As we shall see below, the full integration of the field equations relates these parameters, and for each choice of the coupling functions, the solutions of interest form a family of solutions with only three (continuous) parameters, typically taken to be the global charges ðM; P; QÞ, but possible with nonuniqueness. These reduced quantities are convenient because they are invariant under the scaling symmetry r → λr; ξ → λξ; ð2:15Þ where ξ represents any of the global charges of the model, while fðφÞ and hðφÞ remain unchanged
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