Spontaneous scalarization of charged black holes in the scalar-vector-tensor theory

Abstract

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 ${L}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\alpha}\ensuremath{\beta}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}_{\ensuremath{\alpha}\ensuremath{\beta}}$ 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-Nordstr\"om 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.