Abstract
We investigate the superradiant (in)stability of the extremal multicharge static black holes in the STU supergravity model, which reduce to the Reissner-Nordstr\"om (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 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 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.
Highlights
With the detection of gravitational waves from two merging black holes and photo images of black holes [1,2], an increasing amount of evidence suggests that black holes, predicted by Einstein’s theory of general relativity, exist in our Universe
We study the superradiant instability of the RN black hole from the perspective of more fundamental theories such as strings and supergravities, where the extremal RN black hole emerges as a special Bogomol'nyiPrasad-Sommerfield (BPS) state
We studied superradiant instability by constructing quasibound states of charged Klein-Gordon scalar equation in the background of extremal charged black holes of the STU supergravity model
Summary
With the detection of gravitational waves from two merging black holes and photo images of black holes [1,2], an increasing amount of evidence suggests that black holes, predicted by Einstein’s theory of general relativity, exist in our Universe. The opposite superradiance effect can arise in rotating or charged black holes [3,4,5,6,7], indicating that the scattering process can extract charges and/or angular momenta, and the energies from black holes. A brutal force implementation of the third boundary condition was first introduced by Press and Teukolsky [3] They considered putting a mirror outside the black hole horizon such that the fields would all vanish asymptotically. It turns out the bounded scalar perturbation of a Kerr black hole can be exponentially amplified by extracting energy from the black hole, leading to a bomb effect. We put most of the plots and graphs of numerical results in Appendix C
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