Some Aspects of Spherical Symmetric Extremal Dyonic Black Holes in 4d N = 1 Supergravity

Abstract

In this paper we study several aspects of extremal spherical symmetric black hole solutions of four dimensional N = 1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and non-zero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincides. In addition, we prove the local existence of non-trivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple l C n -models with both linear superpotential and gauge couplings.

Self-gravitating static non-critical black holes in 4D Einstein–Klein–Gordon system with nonminimal derivative coupling

“…This can be seen in two regions, namely in the asymptotic region and the near-horizon region. As mentioned above, we have generally different situations than the case considered, for example in [8,9]. This is so because the scalar field are not frozen near the boundaries which implies the scalar potential cannot be extremized.…”

“…As will be seen in the next section, this setup has a non-critical hairy black hole solution whose hair is said to be secondary-like, since the ansatz (3.1) does not yield any critical solution near the boundaries and moreover, the mass-like quantity of the black hole cannot be a constant but rather depends on ρ in the asymptotic region. Thus this case is different than the case of critical hairy black holes, see for example [8,9]. Let us first discuss some consequences of (3.1).…”

“…Now, we compute a mass-like quantity of the black hole using the Komar integral defined in [9,14]. We obtain a non-constant mass-like quantity…”

“…Comparing (4.6) and (4.15) we can conclude that it is impossible to match up the scalar in both region up to perturbative expansion if the setup (3.1) is fulfilled. However, we could also take the setup discussed in [8,9] where in the asymptotic region the scalar has the form φ(ρ) = φ ∞ + Q/ρ , (4.19) while at the horizon the scalar becomes constant, namely, φ = φ h with constant scalar charge Q. In the latter case, the scalar potential V (φ) in (2.1) should be extremized at the boundaries and moreover, we could have φ ∞ = φ h .…”

“…It turns out that the surface gravity vanishes in this case which follows that we have an ultra-cold black hole [7]. This situation differs from the minimal derivative coupling model considered, for example in [8,9] and the non minimal derivative coupling model discussed in [10]. The structure of the paper can be mentioned as follows.…”