Tachyonic instability of Reissner-Nordström-Melvin black holes in Einstein-Maxwell-scalar theory

In the framework of Einstein-Maxwell-scalar theory, we studied scalar field perturbations Reissner-Nordström-Melvin (RNM) black holes, which describes RN holes immersed in a uniform magnetic field. Due to coupling Maxwell term, acquires an effective mass square which, presence field, will become negative somewhere outside horizon for either sign constant α, thus triggering tachyonic instability and leading spontaneous scalarization when α is large enough. The has significant influences on waveforms onset instability, differs different α. Effects hole charge are also studied.