Quasinormal modes of slowly-spinning horizonless compact objects

One of the main predictions of general relativity is the existence of black holes featuring a horizon beyond which nothing can escape. Gravitational waves from the remnants of compact binary coalescences have the potential to probe new physics at the BH horizons. This prospect is of particular interest given several quantum-gravity models that predict the presence of horizonless compact objects. The membrane paradigm is a generic framework that allows one to parametrise the interior of compact objects in terms of the properties of a fictitious fluid located at the object's radius. It has been used to derive the quasinormal mode spectrum of static horizonless compact objects. Extending the membrane paradigm to rotating objects is crucial to constrain the properties of the spinning merger remnants. In this work, we extend the membrane paradigm to linear order in spin and use it to analyse the relationships between the quasi-normal modes, the reflectivity, and the membrane parameters. We find that the spin tends to increase the damping time of the fundamental mode for reflective ultracompact objects. We also find a breaking of isospectrality between axial and polar modes, and that the spin enhances the deviations from the black hole quasinormal mode spectrum as the compactness decreases. We thus show that spinning horizonless compact objects may be more easily differentiated than nonspinning ones in the prompt ringdown.