A generic feature of nearly out-of-equilibrium dissipative systems is that they resonate through a set of quasinormal modes. Black holes—the absorbing objects par excellence—are no exception. When formed in a merger, black holes vibrate in a process called “ringdown,” which leaves the gravitational-wave footprint of the event horizon. In some models of quantum gravity which attempt to solve the information-loss paradox and the singularities of general relativity, black holes are replaced by regular, horizonless objects with a tiny effective reflectivity. Motivated by these scenarios, here we develop a generic framework to the study of the ringdown of a compact object with various shades of darkness. By extending the black-hole membrane paradigm, we map the interior of any compact object in terms of the bulk and shear viscosities of a fictitious fluid located at the surface, with the black-hole limit being a single point in a three-dimensional parameter space. We unveil some remarkable features of the ringdown and some universal properties of the light ring in this framework. We also identify the region of the parameter space which can be probed by current and future gravitational-wave detectors. A general feature is the appearance of mode doublets which are degenerate only in the black-hole limit. We argue that the merger event GW150914 already imposes a strong lower bound on the compactness of the merger remnant of approximately 99% of the black-hole compactness. This places model-independent constraints on black-hole alternatives such as diffuse “fuzzballs” and nonlocal stars.

• Received 3 July 2020
• Accepted 8 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.064053