Abstract
In this paper, we study the spontaneous scalarization of Reissner–Nordström (RN) black holes enclosed by a cavity in an Einstein–Maxwell-scalar (EMS) model with non-minimal couplings between the scalar and Maxwell fields. In this model, scalar-free RN black holes in a cavity may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. We calculate numerically the black hole solutions, and investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. The scalarized solutions are always thermodynamically preferred over RN black holes in a cavity. In addition, a reentrant phase transition, composed of a zeroth-order phase transition and a second-order one, occurs for large enough electric charge Q.
Highlights
Since it is shown that asymptotically anti-de Sitter (AdS) black holes are thermodynamically stable and the HawkingPage phase transition was revealed in Schwarzschild–AdS black holes [43], thermodynamic properties of various more complicated black holes have been studied [44,45,46,47,48,49,50,51]
It is found that there exist significant differences between the thermodynamic geometry of RN black holes in a cavity and that of RN–AdS black holes [60], and some dissimilarities between the two cases occur for validities of the second thermodynamic law and the weak cosmic censorship [61]
It is shown the black hole bomb still exists for charged black holes in a cavity [64,65,66], the hairy black holes in a cavity are found for Einstein–Maxwell gravity coupled to a charged scalar field [67]
Summary
The EMS model describes a real scalar field minimally coupled to Einstein’s gravity and non-minimally coupled to Maxwell’s electromagnetism. The EMS model is described by the action. Where f (φ) is the coupling function governing the nonminimal coupling of φ and Aμ, Fμν = ∂μ Aν − ∂ν Aμ is the electromagnetic field strength tensor. Ssur f is the surface terms on ∂M, which does not affect the equations of motion. The equations of motion that follow from the action (1) are. The electromagnetic field and the scalar field are given by Aμd xμ = V (r ) dt and φ = φ (r ), respectively. Where primes denote derivatives with respect to the radial coordinate r , and Q is a constant that can be interpreted as the electric charge
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