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 nontrivial electromagnetic field, such as Reissner-Nordström black holes (RN BHs). First, 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 is discussed. Finally, we construct scalarized BH solutions, and investigate their stability.