Critical phenomena of charged Einstein–Gauss–Bonnet black holes with charged scalar hair

Abstract

Einstein-Gauss-Bonnet-gravity (EGB) coupled minimally to a U (1) gauged, massive scalar field possesses -for appropriate choices of the U (1) charge -black hole solutions that carry charged scalar hair if the frequency of the harmonic time-dependence of the scalar field is equal to the upper bound on the superradiant frequency. The existence of these solutions has first been discussed in [63]. In this paper, we demonstrate that the critical value of the scalar charge results from the requirement of non-extremality of the charged black hole solutions and the fact that the scalar field should not escape to infinity. Moreover, we investigate the hairy black holes in more detail and demonstrate that the branch of these solutions joins the branch of the corresponding charged EGB black hole for vanishing scalar field, but is not connected to the branch of boson stars in the limit of vanishing horizon radius. This indicates that it is unlikely that these black holes appear from the collapse of the corresponding boson stars. Finally, we prove a No-hair theorem for charged scalar fields with harmonic time-dependence for static, spherically symmetric, asymptotically flat electro-vacuum black holes in d space-time dimensions and hence demonstrate that the GB term is crucial for the existence of the hairy black holes discussed in this paper.

Large and ultracompact Gauss-Bonnet black holes with a self-interacting scalar field

“…for all forms of the coupling function f (φ), with D being the scalar charge, as found in [39]. For Λ < 0 and V (φ) = 1, black-hole solutions with an asymptotically Anti-de Sitter behaviour are expected to emerge as in [60,160]. These solutions do not possess a scalar charge since the asymptotic behaviour of the scalar field is given by the expression…”

“…For V (φ) = 1, the expression of C may take the form of a second-order polynomial foṙ f 2 h , which then leads to two branches of black-hole solutions (or four, if negative values oḟ f h are also allowed) describing solutions having either a minimum or a maximum horizon radius [60,160]. In reality, only solutions with a minimum horizon radius are found while the second branch is plagued by instabilities.…”

Diving inside a hairy black hole

“…Even if this does not seem to be the case for a minimally coupled scalar in Einstein-Maxwell theory [18], there are simple enough extensions that do present hairy solutions. That is precisely the case for charged Einstein-Gauss-Bonnet black holes in 4 + 1 dimensions [19,20], which represent a good playground to test these ideas. This is what this paper is about.…”

Spinning-charged-hairy black holes in 5D Einstein gravity

“…Recently it was shown [20] that, in d=5, non-spinning hairy black holes exist in the Einstein-Gauss-Bonnet-Maxwell theory provided both -the gauge coupling constant and the Gauss-Bonnet parameters-are sufficiently large. Several properties of these solutions have been discussed in [21]. To our knowledge, the gauge version of d=5 spinning black holes has not yet been studied and this problem in emphasized in this paper.…”