Gravitational electric-magnetic duality at the light ring and quasinormal mode isospectrality in effective field theories

TL;DR

This paper explores how gravitational electric-magnetic duality at the light ring enforces quasinormal mode isospectrality in effective field theories, linking duality symmetry to spectral properties of black hole perturbations.

Contribution

It demonstrates that gravitational electric-magnetic duality at the light ring underpins isospectrality and constrains higher-derivative corrections in effective field theories of gravity.

Findings

Duality enforces isospectrality in the eikonal limit.

Higher-derivative corrections preserving duality maintain isospectrality.

Duality at the light ring constrains effective field theory couplings.

Abstract

Black hole perturbations are characterized by a superposition of damped exponentials known as quasinormal modes. In general relativity, the spectra of parity-even and parity-odd quasinormal modes coincide -- a property known as isospectrality, which is typically broken by corrections beyond general relativity. Recently, certain higher-derivative operators were shown to preserve isospectrality in the high-frequency (eikonal) regime. Motivated by the relation between the light ring Penrose limit and the eikonal limit, we study isospectrality in a class of plane-wave spacetimes. In general relativity, we show that dynamical metric fluctuations on these backgrounds admit a gravitational analog of electric-magnetic duality, which enforces isospectrality. Requiring this duality to persist in the presence of higher-derivative corrections constrains the couplings so that isospectrality is preserved. We conclude that gravitational electric-magnetic duality at the light ring is the organizing principle behind isospectrality in the eikonal limit, and we conjecture that this remains true for other duality-invariant corrections to general relativity.