Black Hole Ringdown Amplitudescopy

TL;DR

This work addresses how beyond-GR physics manifests in black hole ringdowns via two signatures: shifts of Kerr quasinormal-mode frequencies and the emergence of extra field-induced modes. It introduces a theory-agnostic ringdown amplitudes framework (ringdown amplitudescopy) in which beyond-GR effects enter primarily through the amplitudes and phases of extra-field modes, while GR-like QNM frequencies remain tied to Kerr values; for dynamical Chern-Simons and Einstein-scalar-Gauss-Bonnet theories, the deviations scale with a dimensionless coupling ζ and scalar-mode amplitudes with γ, enabling concrete forecasts. Using O4-like mock data and an ET-era forecast, the paper demonstrates that including extra scalar modes yields tighter constraints on the couplings and can prevent bias that arises when these modes are neglected, even at modest SNRs; it also shows that higher modes and scalar modes together can break parameter degeneracies and enable robust tests of GR. The findings argue for incorporating extra-field-mode templates in current and future gravitational-wave analyses, outline extensions to other field content and precession, and highlight the need for NR-informed excitation amplitudes to fully exploit ringdown observations for high-precision tests of gravity.

Abstract

Black hole ringdowns in extensions of General Relativity (GR) generically exhibit two distinct signatures: (1) theory-dependent shifts in the standard black-hole quasinormal modes, and (2) additional modes arising from extra fundamental fields --such as scalar, vector, or tensor degrees of freedom-- that can also contribute to the gravitational-wave signal. As recently argued, in general both effects are present simultaneously, and accurately modeling them is essential for robust tests of GR in the ringdown regime. In this work, we investigate the impact of extra field-induced modes, which are often neglected in standard ringdown analyses, on the interpretation of gravitational-wave signals. To provide some concrete examples, we focus on dynamical Chern-Simons and Einstein-scalar-Gauss-Bonnet theories, well-motivated extensions of GR, characterized respectively by a parity-odd and a parity-even coupling between a dynamical scalar field and quadratic curvature invariants. We show that including extra field-induced modes improves the bounds on these theories compared to standard spectroscopy and also allows for equally constraining complementary tests not based on quasinormal mode shifts. Our analysis highlights the relevance of incorporating extra field-induced modes in ringdown templates and assesses their potential to either bias or enhance constraints on GR deviations.

Figures (3)

• Figure 1: Fits for the corrections to the QNM frequency and damping time as a function of the spin $\chi$ for CS gravity Chung:2025gyg (continuous lines) and GB gravity Chung:2024vaf (dashed lines). For each theory, we show the deviations of the $(220)$ (blue) and $(330)$ (purple) modes. Dotted and continuous curves refer to axial and polar modes, respectively.
• Figure 2: Distributions of $\ell_{\rm GB}$ (left panels) and $\ell_{\rm CS}$ (right panels) for $\frac{A_{220,A}}{A_{220_P}}=0.25$. Top and down panels represent the cases of $\gamma=\gamma_{\rm inj}$, and $\gamma=0$, respectively. We assume ${\rm SNR}=20$ with the O4 LVK network. The prior on $\ell_{\rm GB/CS}$ is uniform in the range $[0,60]\,{\rm km}$.
• Figure 3: Distributions of $\ell_{\rm GB}$ (left panels) and $\ell_{\rm CS}$ (right panels) for $A_{R, 330}=\frac{A_{330}}{A_{220}}=[0.005,0.351,0.4]$ (in blue, red, and green, respectively). Each row refers to a different value of injected $\gamma$ (from top to bottom: $\gamma_{\rm inj}=0,1, 5, 10$. The continuous and dashed distributions correspond to a recovery with $\gamma=\gamma_{\rm inj}$ and $\gamma=0$, respectively. In the GB case, the priors are uniform across $\ell_{\rm GB}\in[0,16]\,{\rm km}$ and $M\in[15,40]M_{\odot}$ while in the CS case they are uniform across $\ell_{\rm CS}\in[0,20]\,{\rm km}$ and $M\in[17,40]M_{\odot}$.