Suppression of Gravitational-Wave Echoes in Diffeomorphism-Invariant Nonlocal Gravity

TL;DR

The paper shows that in covariant nonlocal gravity theories constructed from analytic entire functions of the covariant d'Alembertian, Paley–Wiener bounds enforce exponential damping of high-frequency reflections and smear sharp interior potentials, thereby suppressing gravitational-wave echoes for both horizon-bearing and horizonless remnants. The nonlocal regulator acts as a frequency filter, yielding a factor $\tilde{K}_{\Lambda_G}(2\omega)$ that multiplies local reflection amplitudes, with a Gaussian regulator giving $|\tilde{K}_{\Lambda_G}(2\omega)| = e^{-4\omega^2/\Lambda_G^2}$. Consequently, the echo train is exponentially attenuated in frequency and broadened in time by $\Delta t \sim \Lambda_G^{-1}$, and horizons remove the inner cavity altogether while horizonless interiors still experience strong nonlocal suppression. These results imply that the non-detection of echoes does not favor classical horizons and instead provides a consistency check on the analytic structure and nonlocal scale of quantum gravity in the strong-field regime. The study highlights how ringdown phenomenology encodes fundamental quantum-gravity requirements and places bounds on the nonlocal completion of gravity.

Abstract

Searches for late--time gravitational--wave echoes following compact binary mergers are often interpreted as probes of exotic near--horizon or horizonless physics. We show that a well--motivated class of ultraviolet--finite quantum gravity and modified gravity theories, those based on diffeomorphism--invariant, analytic, entire--function nonlocality, generically suppress observable echo signals. The suppression follows from Paley--Wiener bounds associated with the analyticity of the nonlocal regulator, which enforce exponential damping of high--frequency reflection amplitudes and smear sharp effective potentials in the black--hole interior. We demonstrate that for regular black holes with horizons, the standard ingoing boundary condition eliminates the cavity required for echoes, while for regular horizonless compact objects the nonlocal kernel strongly attenuates both inner and photon--sphere reflections. As a result, repeated reflections during the ringdown phase are exponentially suppressed in frequency space and washed out in the time domain. Our results imply that the absence of echoes in current gravitational--wave data is consistent with covariant nonlocal gravity theories and does not, by itself, favor classical horizons over regular or horizonless ultraviolet completions. The analyticity and Paley--Wiener bounds that enforce echo suppression are required to ensure unitarity, ghost freedom, and ultraviolet finiteness of the underlying quantum theory. As a result, the classical ringdown phenomenology already encodes quantum--gravity consistency conditions. We emphasize that the absence of echoes in such theories does not rely on quantum decoherence or stochastic effects, but instead reflects the analytic structure imposed by quantum gravity on the classical limit.