Abstract
We investigated the superradiance and stability of the regularized 4D charged Einstein-Gauss-Bonnet black hole which is recently inspired by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. We found that the positive Gauss-Bonnet coupling constant α enhances the superradiance, while the negative α suppresses it. The condition for superradiant instability is proved. We also worked out the quasinormal modes (QNMs) of the charged Einstein-Gauss-Bonnet black hole and found that the real part of all the QNMs does not satisfy the superradiance condition and the imaginary parts are all negative. Therefore this black hole is stable. When α makes the black hole extremal, there are normal modes.
Highlights
Agree well and support the existence of superradiation in RN black hole geometry mutually
We have shown the superradiance of the 4D charged EGB black hole under the charged scalar perturbation
We studied the parameter region of the regularized 4D charged EGB black hole where allows the event horizon
Summary
The action of the EGB gravity with electromagnetic field in D-dimensional spacetime has the form. The term Hμν comes from the variation of the Gauss-Bonnet term, which is a topological invariant term in four dimension. The Gauss-Bonnet term gives rise to non-trivial dynamics and regularized black hole solutions were discover recently [17, 28]. The spherically symmetric charged black hole solution of (2.3) in four dimension has the form ds2 = −f (r)dt2 + 1 dr2 + r2(dθ2 + sin θdφ2), f (r). In the vanishing limit of α and in the far region, only the negative branch recovers the Reissner-Nordstrom (RN) black hole. The solution has at most two horizons in appropriate parameter region, r± = M ± M 2 − Q2 − α. Note that when Q > 1, the solution has no RN black hole limit since α cannot tend to 0 now. It is necessary and important to study the stability of black holes under various kinds of perturbation since black holes usually behave differently for different kinds of perturbation
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