Spontaneous scalarization of charged black holes in the Scalar-Vector-Tensor theory

We present spontaneous scalarization of charged black holes (BHs) which is induced by the coupling of the scalar field to the electromagnetic field strength and the double-dual Riemann tensor $L^{\mu\nu\alpha\beta}F_{\mu\nu}F_{\alpha\beta}$ in a scalar-vector-tensor theory. In our model, the scalarization can be realized under the curved background with a non-trivial electromagnetic field, such as Reissner-Nordstr$\ddot{\rm o}$m Black Holes (RN BHs). Firstly, we investigate the stability of the constant scalar field around RN BHs in the model, and show that the scalar field can suffer a tachyonic instability. Secondly, the bound state solution of the test scalar field around a RN BH and its stability are discussed. Finally, we construct scalarized BH solutions, and investigate their stability.