Spontaneous scalarization of charged Reissner-Nordström black holes: Analytic treatment along the existence line

• Published in: Physics letters. B Vol. 798; p. 135025
• Main Author: Hod, Shahar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 10.11.2019; Elsevier
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2019.135025

It has recently been demonstrated that charged black holes can support spatially regular matter configurations made of massless scalar fields which are non-minimally coupled to the electromagnetic field of the charged spacetime. Intriguingly, using numerical techniques, it has been revealed that the resonant spectra of the composed charged-black-hole-nonminimally-coupled-scalar-field configurations are characterized by charge-dependent discrete scalarization bands α∈{[αn−(Q¯),αn+(Q¯]}n=0n=∞, where α is the dimensionless coupling constant of the theory and Q¯≡Q/M is the dimensionless charge-to-mass ratio of the central supporting black hole. In the present paper we use analytical techniques in order to study the physical and mathematical properties of the spatially regular non-minimally coupled scalar field configurations (linearized scalar clouds) which are supported by the central charged Reissner-Nordström black holes. In particular, we derive a remarkably compact formula for the discrete resonant spectrum {αn−(Q¯)}n=0n=∞ which characterizes the composed black-hole-linearized-field configurations along the existence-line of the system, the critical line which separates bare Reissner-Nordström black holes from hairy scalarized black-hole configurations. The analytical results are confirmed by direct numerical computations.