EFT Corrections to Charged Black Hole Quasinormal Modes

TL;DR

This work analyzes how higher-derivative Effective Field Theory (EFT) corrections modify the quasinormal mode (QNM) spectrum of near-extremal Reissner–Nordström black holes. By deriving an EFT-corrected Moncrief equation and solving it analytically and numerically, the authors compute corrected QNM frequencies and examine the so-called zero-damped modes (ZDMs) that dominate near extremality, including the lifting of degeneracy between axial and polar sectors. They also test the Quasinormal Mode Causality bound by incorporating Standard Model contributions (notably from integrating out the electron), finding that the bound holds (with a characteristic causality parameter $\rho$ negative or vanishing for ZDMs). The results illuminate the interplay between EFT, extremal black hole dynamics, and causality, and lay groundwork for extending the analysis to rotating (Kerr–Newman) or AdS settings and for potential observational implications in gravitational-wave data.

Abstract

We study the impact of higher-derivative corrections from Effective Field Theory on the quasinormal mode spectrum of Reissner-Nordström black holes. While previous work has explored corrections to Schwarzschild and Kerr black holes - typically using small-rotation approximations - a comprehensive analysis near extremality remains lacking. We focus on Reissner-Nordström black holes as a tractable model admitting an extremal limit, enabling investigation of the effect of these corrections on the so-called zero damped modes, which dominate in this regime. Specifically, we derive a corrected Moncrief equation governing quasinormal modes and present both analytic and numerical results for the corrected frequencies. This work also offers the first explicit test of the recently proposed "Quasinormal Mode Causality" bound arXiv:2401.05524, which constrains Effective Field Theory coefficients by requiring that quasinormal mode lifetimes do not increase measurably under ultraviolet-complete Effective Field Theory corrections. Using Standard Model contributions - particularly those arising from integrating out the electron - we verify that this bound holds. Our results provide new insights into the interplay between Effective Field Theory, extremal black hole dynamics, and causality in gravitational theories.

Figures (4)

• Figure 1: EFT Corrections in the microcanonical ensemble, to the longest lived ( i.e. smallest $|\text{Im}(\omega_0 M_0)|$) damped mode in the $\ell=2$, $Z_2^-$ sector, as a function of $M \kappa_0$.
• Figure 3: EFT Corrections in the canonical ensemble, to the longest lived ( i.e. smallest $|\text{Im}(\omega_0 M_0)|$) damped mode in the $\ell=2$, $Z_2^-$ sector, as a function of $M_0 \kappa$.
• Figure 5: EFT Corrections in the canonical ensemble, to the lowest ZDM $\ell=2, g=2$ axial $(-)$ QNM, as a function of $M_0 \kappa$. The red discs give the analytical predictions for the $y$-intercepts of these lines.
• Figure 6: We plot $\rho_{0,6,9}$, defined in Eq. (\ref{['eq:causa']}), over a range of temperatures. This is done for the longest lived damped mode in the relevant sectors.