Superradiant Instability of Extremal Black Holes in STU Supergravity

TL;DR

This paper analyzes the superradiant stability of extremal black holes in the STU supergravity model, revealing that unequal charges lead to instability, unlike the fine-tuned RN black hole.

Contribution

It provides a detailed study of superradiant instability in multi-charge extremal black holes within STU supergravity, highlighting the role of charge configurations.

Findings

Unequal charges cause superradiant instability in extremal black holes.

Trapping-well configurations can have single or double peaks.

Superradiant instability occurs unless all charges are equal.

Abstract

We investigate the superradiant (in)stability of the extremal multi-charge static black holes in the STU supergravity model, which reduce to the RN black hole when all the charges are equal. We first show that the frequency of quasi-bound states is necessarily complex and obtain the corresponding superradiant condition. We then study the effective potential of the Schr\"odinger-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 quasi-bound 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.