Conditions for Gravitational-Wave Echo Suppression in Diffeomorphism-Invariant Nonlocal Quantum Gravity

Abstract

Gravitational-wave echoes can arise when perturbations are trapped between distinct scattering structures in the effective potential of an ultracompact merger remnant. We examine the conditions under which analytic nonlocal smearing can reduce such signals in a Gaussian-smeared regular compact-object geometry. For configurations possessing a true event horizon, the standard purely ingoing boundary condition excludes an inner echo cavity independently of the ultraviolet completion. For horizonless configurations, smoothness alone does not eliminate echoes. The axial Regge--Wheeler potential can contain a trapping region bounded by an inner centrifugal barrier and an outer potential maximum. We distinguish echoes caused by the global geometric potential from reflection by an additional localized inner transition layer. If such a layer is smeared over a proper radial length $\ellNL$ and the metric function is approximately constant across it, its tortoise-coordinate width is enhanced by the gravitational redshift. In the weak-scattering approximation, a Gaussian layer produces the conditional suppression. This result requires a localized weak interaction, slow variation of the background across the layer, and a valid Born approximation. It is not a model-independent exclusion of echoes from smooth horizonless objects. The analysis identifies the redshift, nonlocal-length, and potential-structure conditions that must be evaluated before gravitational-wave observations can be converted into constraints on analytic nonlocal quantum gravity.