Scalarization of charged Taub-NUT black hole and the entropy bound

Abstract

We investigate the spontaneous scalarization of charged Taub-NUT black holes within the framework of Einstein-Maxwell-scalar-Gauss-Bonnet gravity. By selecting a suitable coupling function, the theory admits the analytic charged Taub-NUT geometry as a solution. We demonstrate that this scalar-free background becomes unstable within specific parameter regimes, leading to the bifurcation of a new branch of hairy charged Taub-NUT black holes. These solutions are characterized by a two-dimensional parameter space spanned by the electric charge and the NUT parameter. We conduct a systematic study of their properties, specifically the scalar charge, temperature, and entropy. Our analysis reveals that the entropy of the scalarized solutions exhibits particularly compelling features. Two universal characteristics emerge: first, the entropy of the hairy black hole is strictly greater than that of its scalar-free counterpart; second, the entropy reaches a local maximum precisely at the bifurcation point. Notably, when the electric charge is fixed, this maximum entropy value remains universal across a specific range of the mass parameter.

Figures (10)

• Figure 1: The existence line for fixed $q/\lambda\,$, fixed $n/\lambda \,$ and $n = q$.
• Figure 2: The scalar charge parameter $D$ of the hairy charged Taub-NUT black hole as a function of its mass parameter $m$, with the ratio $q/\lambda$ fixed at $1/4$ and various values of the NUT parameter $n$. The $D$-$m$ curves for which the value of $m$ at the bifurcation point is greater than zero are shown in the left panel (a), while those for which this value is less than zero are presented in the right panel (b).
• Figure 3: The scalar charge parameter $D$ of the black hole is plotted as a function of its event horizon radius $r_h$. The $D$-$r_h$ curves corresponding to small values of the NUT parameter $n$ are shown in panel (a), where all curves exhibit only a single branch; by contrast, those for larger values of $n$ are presented in panel (b).
• Figure 4: $S/\lambda^2$ as a function of $r_h/\lambda$ for fixed $q/\lambda = 1/4$. Dashed lines denote charged scalarized black holes, while solid lines denote scalar-free Taub–NUT black holes for the same NUT parameter $n$.
• Figure 5: $S/\lambda^2$ as a function of $m/\lambda$ for different values of the charge parameter. Dashed lines and solid lines correspond to charged scalarized black holes and scalar-free Taub–NUT black holes with the same NUT parameter $n$, respectively.