Superradiant instability of extremal black holes in STU supergravity

We investigate the superradiant (in)stability of the extremal multicharge static black holes in the STU supergravity model, which reduce to the Reissner-Nordstrom (RN) black hole when all the charges are equal. We first show that the frequency of quasibound states is necessarily complex and obtain the corresponding superradiant condition. We then study the effective potential of the Schrodinger-like equation associated with the radial function of the charged scalar field. We find that trapping-well configurations can emerge with either a single peak or double peaks. We numerically obtain the corresponding unstable quasibound states, organized under the overtone number, as well as how the charged black holes deviate from the RN black hole. We find that the STU black holes are superradiantly unstable as long as not all the charges are equal, indicating that the superradiant stability of the extremal RN black hole is a fine-tuning result in the framework of the STU supergravity model.

Automated summary

In this study, we investigate the superradiant (in)stability of extremal multicharge static black holes in the STU supergravity model. We show that the frequency of quasibound states is complex and derive the corresponding superradiant condition. By examining the effective potential of the Schrodinger-like equation, we find trapping-well configurations with either a single peak or double peaks. Numerical calculations reveal the unstable quasibound states and the deviation of charged black holes from the RN black hole. The results indicate that the superradiant stability of extremal RN black hole is a fine-tuning result in the framework of the STU supergravity model.