Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors

TL;DR

This paper analyzes the excitation, stability, and gravitational wave signatures of ultracompact horizonless objects, highlighting the role of long-lived modes, echoes, and greybody factors through analytical and numerical methods.

Contribution

It introduces a practical waveform model combining black hole and cavity modes, and extends greybody factor analysis to exotic objects, enhancing understanding of their spectral and gravitational wave features.

Findings

Long-lived modes are weakly excited and dominate late-time echoes.

Echo signals are structured with prompt ringdown, early echoes, and late-time long-lived modes.

Greybody factors remain stable under small potential deformations.

Abstract

We present an analytical and numerical investigation of the quasinormal excitation factors of ultracompact horizonless objects. These systems possess long lived quasinormal modes with extremely small imaginary parts, originating from the effective cavity between the photon sphere and the object's interior. We show that the excitation of such modes is strongly suppressed, scaling with the imaginary part of their frequency, and therefore they contribute to the waveform only at very late times. This hierarchy naturally explains the structure of echo signals: the prompt ringdown is dominated by standard light ring modes, the early echoes arise from moderately damped cavity modes, and only the latest echoes are governed by long lived modes. Based on this, we propose a practical ringdown waveform model based on a superposition of ordinary black hole quasinormal modes and cavity modes, which captures the complexity of the ringdown of horizonless ultracompact objects. We further demonstrate that the combination of small excitation factors and weak damping enhances the robustness of long lived modes against localized perturbations, in contrast to the spectral instabilities affecting standard black hole quasinormal modes. Finally, we extend the analysis of greybody factors to exotic compact objects and wormholes, showing that they remain stable under small deformations of the effective potential and thus represent robust observables. Our results provide a unified framework for understanding excitation, stability, and echoes in ultracompact horizonless objects, with direct implications for their spectral properties and gravitational wave signatures.