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.