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Quasinormal modes of Gauss-Bonnet black holes via the spectral method: Scalar, vector, and tensor perturbations
Phys. Rev. D 114, 044015 – Published 6 August, 2026
DOI: https://doi.org/10.1103/91q6-r3jd
Abstract
We present a unified study of scalar, vector, and tensor quasinormal modes (QNMs) of Schwarzschild black holes corrected by a Gauss-Bonnet (GB) term in higher dimensions. Using a high-precision Chebyshev spectral method, we map the QNM spectra across well beyond the regime where sixth-order Wentzel-Kramers-Brillouin and characteristic-integration techniques remain reliable. Across the three spin sectors, we find several robust signatures of higher-curvature dynamics: the appearance of overdamped purely imaginary modes, nonmonotonic behavior in the real parts of higher overtones, and a strong amplification of the dimensionless QNM frequencies in string-motivated dimensions. In the scalar and vector sectors, we uncover an exact isospectrality between the scalar monopole () and vector dipole () at vanishing GB coupling, and we provide an analytic proof based on a Darboux factorization of the corresponding Hamiltonians. In the tensor sector, we obtain the first numerical confirmation of the long-predicted instability in six dimensions; its onset is sharply captured by the Cohn-Calogero bound and leads to the mass threshold . No analogous instability is found for , and no tensor isospectrality occurs. Converting the dimensionless frequencies to physical units suggests that the amplified modes in higher dimensions may enter the sensitivity window of future space-based detectors such as DECIGO. The merged analysis provides a comprehensive benchmark for QNMs in Einstein-Gauss-Bonnet gravity and highlights the limitations of standard approximation schemes in the strong-coupling and high-overtone regimes.
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