Quasinormal Modes of Gauss–Bonnet Black Holes via the Spectral Method: Scalar, Vector, and Tensor Perturbations

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 $D\in\{5,6,7,8,10,11,12,26\}$ well beyond the regime where sixth-order WKB 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, non-monotonic behaviour 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 ($\ell=0$) and vector dipole ($\ell=1$) at vanishing GB coupling, and we provide an analytic proof based on a Darboux factorisation 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 $GM\leq 158.1\,α^{3/2}$. No analogous instability is found for $D\geq 7$, 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.

Keywords

Bibliographic record

BibTeX Citation

@article{Batic2026quasinormalmodes,
  author = {Batic, D. and Dutykh, D.},
  title = {Quasinormal Modes of Gauss–Bonnet Black Holes via the Spectral Method: Scalar, Vector, and Tensor Perturbations},
  journal = {Phys. Rev. D},
  year = {2026},
  volume = {114},
  number = {4},
  pages = {044015},
  doi = {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 $D\in\{5,6,7,8,10,11,12,26\}$ well beyond the regime where sixth-order WKB 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, non-monotonic behaviour 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 ($\ell=0$) and vector dipole ($\ell=1$) at vanishing GB coupling, and we provide an analytic proof based on a Darboux factorisation 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 $GM\leq 158.1\,α^{3/2}$. No analogous instability is found for $D\geq 7$, 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.},
  keywords = {quasinormal modes, Gauss–Bonnet black holes, spectral method, scalar perturbations, vector perturbations, tensor perturbations, Chebyshev polynomials, black hole physics},
  publisher = {American Physical Society (APS)},
  issn = {2470-0010}
}