Causality and quasi-normal modes in the GREFT

Abstract

The General Relativity Effective Field Theory (GREFT) introduces higher-derivative interactions to parameterise the gravitational effects of massive degrees of freedom which are too heavy to be probed directly. The coefficients of these interactions have recently been constrained using causality: both from the analytic structure of 4-point graviton scattering and the time delay of gravitational waves on a black hole background. In this work, causality is used to constrain the quasi-normal mode spectrum of GREFT black holes. Demanding that quasi-normal mode perturbations decay faster in the GREFT than in General Relativity -- a new kind of causality condition which stems from the analytic structure of 2-point functions on a black hole background -- leads to further constraints on the GREFT coefficients. The causality constraints and compact expressions for the GREFT quasi-normal mode frequencies presented here will inform future parameterised gravitational waveforms, and the observational prospects for gravitational wave observatories are briefly discussed.