Spontaneous scalarization of dyonic black hole in Einstein–Maxwell-scalar theory

Abstract

In this paper, we study the scalarization of the static and spherically symmetric dyonic Reissner–Nordstrom (RN) black holes in the Einstein–Maxwell-scalar theory where the scalar field is coupled to an electromagnetic Chern–Simons term. When both electric and magnetic charges are present, there exists an unstable region of parametric space for the dyonic RN black holes where the scalarization of black holes should occur. That is to say, mixing electric and magnetic charges can reduce the scalarization in this theory. Firstly, we calculate the perturbation field equations under the dyonic RN black hole background and obtain the corresponding asymptotic-flat perturbation solutions, which are the bifurcation points at the dyonic RN branch. The results show that the perturbation scalarization demands a lower bound of the coupling constant. Then, we calculate the scalarized black hole solutions bifurcating from the dyonic RN solutions. We find that there exist a lot of discrete branches of the scalarized solutions. Contract to the dyonic RN solutions, these scalarized solutions can be overcharged and their mass could even approach zero. After illustrating the behavior of the entropy for the scalarized black holes, we demonstrate that the scalarized configurations might be thermodynamically more stable than GR configurations. Moreover, we also show that for each scalarized branch, the black hole cannot reach the extremal limit with vanishing temperature.