Quasinormal modes of rotating black holes in shift-symmetric Einstein-scalar-Gauss-Bonnet theory

TL;DR

This paper computes the full non-perturbative quasinormal-mode spectrum of rapidly rotating black holes in shift-symmetric EsGB theory using a spectral method, extending beyond prior quadratic-in-coupling perturbative results. By solving a seven-function perturbation system on a compactified grid and enforcing correct ingoing/outgoing wave behavior, the authors obtain accurate QNM frequencies across the domain of black-hole existence and compare them with weak-coupling predictions and with EdGB results. Key findings include the breaking of isospectrality between axial and polar modes, mode mixing (including scalar-led contributions), and significant deviations from perturbative results as the coupling grows or rotation increases; near the domain boundary, numerical precision becomes challenging. The work provides practical fitting formulas and highlights implications for gravitational-wave tests of gravity, offering a benchmark for non-GR signatures in ringdown signals.

Abstract

We employ a recently developed spectral method to obtain the spectrum of quasinormal modes of rapidly rotating black holes in alternative theories of gravity and apply it to the black holes of shift-symmetric Einstein-scalar-Gauss-Bonnet theory. In this theory the quasinormal modes were recently obtained by employing perturbation theory in quadratic order in the Gauss-Bonnet coupling constant. Here we present the full non-perturbative results for the spectrum within the domain of existence of rotating black holes and compare with the perturbative results. We also compare with the quasinormal mode spectrum of rapidly rotating Einstein-dilaton-Gauss-Bonnet black holes.

Figures (4)

• Figure 1: The domain of existence of rotating black hole solutions in shift-symmetric EsGB theory showing the dimensionless angular momentum $J/M^2$ versus the dimensionless coupling constant $\alpha/M^2$. The boundary consists of extremal, critical, static, and Kerr black holes. (Data extracted from Delgado:2020rev).
• Figure 2: Fundamental shift-symmetric EsGB ($l=2$) and ($l=3$)-led modes for $M_z=2$: scaled real part $M\omega_R$ (left column) and scaled imaginary part $M\omega_I$ (right column) of the polar-led, axial-led, and scalar-led quasinormal modes as a function of the scaled coupling constant $\alpha/M^2$ for scaled angular momenta $J/M^2=0, 0.2, 0.4, 0.6, 0.8$ (from top to bottom). The limiting coupling constant for each value of $J/M^2$ of the background black holes is shown by the dark khaki vertical line.
• Figure 3: Comparison of the exact modes with $l=M_z=2$ fundamental polar-led and axial-led quasinormal modes where a weak coupling (WC) approximation was employed Chung:2024ira, for ${J/M^2}=0.2,0.4,0.6,0.8$. Also shown is a comparison between the static modes with a full coupling and the perturbative modes for a small scaled angular momentum ${J/M^2}=0.005$ (topmost) Chung:2024ira.
• Figure 4: Comparison between the $l=M_z=2$ fundamental polar-led and axial-led modes of the shift-symmetric EsGB black holes (ss) and EdGB black holes (dil) Blazquez-Salcedo:2024oekBlazquez-Salcedo:2024dur, for ${J/M^2}=0.2, 0.8$.