Dyonic Einstein-Maxwell-scalar black holes: the cold, the hot and the plunge

Abstract

We investigate dyonic nonlinearly scalarized black holes in Einstein-Maxwell-scalar theory. The domain of existence of scalarized dyonic black holes consists of three branches. The cold branch and the hot branch bifurcate at a minimal value of the charge, analogous to the purely electrically charged scalarized black holes. However, the presence of both charges allows for regular extremal black holes, leading to a third branch featuring a sudden plunge in Hawking temperature. In fact, the presence of both electromagnetic charges introduces a factor $Δ(φ)$ in the source term of scalar field equations that vanishes when the coupling function $f(φ)$ equals the ratio of the charges for some value of the scalar field $φ_c$. The scalar field of extremal black holes assumes precisely this value at the horizon, $φ_H=φ_c$. We demonstrate the plunge for the coupling function $f(φ)=\exp(αφ^3)$.

Figures (3)

• Figure 1: (a) The dimensionless horizon area $a_H$ is shown versus the charge parameter $q$. (b) The dimensionless temperature $t_H$ is shown vs the charge parameter $q$.
• Figure 2: (a) The dimensionless temperature $t_H$ is shown vs the scalar field at the horizon $\phi_H$. (b) The dimensionless temperature $t_H$ is shown vs the horizon area $a_H$.
• Figure 3: (a) The factor $(1- (\beta f(\phi_H))^2)$ of $\Delta(\phi_H)$ is shown on a logarithmic scale vs the dimensionless horizon area $a_H$ for $\alpha=20$, $\beta=0.05$. (b) The scalar field $\phi(x)$ is shown vs the compactified dimensionless radial coordinate $x=1-\frac{r_H}{r}$ for the last few values of the electric potential at the horizon $V_H$ close to the extremal black hole solution for $\alpha=20$, $\beta=0.05$.