Amplification of new physics in the quasinormal mode spectrum of highly-rotating black holes

TL;DR

The paper investigates how small higher-derivative corrections to GR modify the quasinormal-mode spectrum of near-extremal Kerr black holes. Using a quartic-curvature EFT that preserves isospectrality in the eikonal limit, it shows that modes near the phase boundary between zero-damping and damped families experience amplified, potentially order-one, corrections due to a shifted phase boundary, even within a controlled EFT regime. An exact near-extremality analysis reveals how the boundary shifts as $\mu_{\rm cr}=\bar{\mu}_{\rm cr}+\hat{\alpha}\delta\mu_{\rm cr}$, causing some modes to cross the boundary and change the number of DMs. The work further argues, via Wilsonian and self-consistency arguments, that these effects can occur without EFT breakdown and highlights the observational significance: near-extremal black-hole spectroscopy could be a powerful probe of new gravitational physics, with certain low-$l$ modes showing especially large sensitivity.

Abstract

We show that perturbatively-small higher-derivative corrections to the Einstein-Hilbert action can lead to order-one modifications of the quasinormal mode spectrum of near-extremal Kerr black holes. The spectrum of such black holes contains zero-damping modes (ZDMs) and damped modes (DMs), with the latter only existing when the ratio $μ=m/(l+1/2)$ is below a critical value $\barμ_{\rm cr}\approx 0.744$. Thus, this value represents a "phase boundary" that separates a region with both ZDMs and DMs and a region with only ZDMs. We find that the modes lying close to the phase boundary are very sensitive to modifications of GR, as their lifetimes receive corrections inversely proportional to their distance to the boundary. We link this growth of the corrections to a modification of the critical point $\barμ_{\rm cr}$, which can lead to a change in the number of DMs and produce order-one effects in the spectrum. We show that these large effects can take place in a regime in which the higher-derivative expansion remains under control. We also perform an exact analysis of the modification of the phase boundary for lower $(l,m)$ modes and pinpoint those that are most sensitive to corrections. Our results indicate that spectroscopy of highly-rotating black holes is by far the most powerful way to search for new physics in ringdown signals.

Figures (2)

• Figure 1: Relative corrections to the imaginary part of the QNM frequencies as a function of the dimensionless spin $\chi=a/M$ for several values $\mu\ge \bar{\mu}_{\rm cr}$. The corrections become arbitrarily large when $\mu$ approaches $\bar{\mu}_{\rm cr}$ and we take $\chi\to 1$ (observe that the plot is in a log-log scale). For $\mu= \bar{\mu}_{\rm cr}$ (dashed line), the relative corrections diverge at extremality --- see (\ref{['relII']}).
• Figure 2: Coefficient $\Delta_{l m}^{+}$ for the relative corrections to near-extremal QNMs in the theory (\ref{['eq:ISO']}). The color of the markers represents the magnitude of $\Delta_{l m}^{+}$ in a logarithmic scale. Triangles are $(l, m)$ values for which only ZDMs exist in GR and circles are values for which DMs exist. The most sensitive modes (in darker red) are precisely those on the boundary from one region to another.