How does a dark compact object ringdown?

Abstract

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.

Tidal-heating/viscous dissipation correspondence in black holes and viscous compact objects

“…5 We assume that the extrinsic curvature of the interior is zero [33]. 6 The results agree with [60] for 1, where here we also neglected the bulk viscosity since it is insignificant to the absorption coefficient in the BH limit.…”

“…(2.8), for the case of our interest we consider zero bulk viscosity which found to be negligible when 1. The function is taken from the Appendix of [60] Where w = M ω and ω = 2Ω is twice the orbital frequency. = ∆R/R = (R − 2M )/2M is the deviation from the BH horizon.…”

“…This implies that a perfect absorber with γ U CO = 1 has R = 0 which corresponds to η U CO = η BH , alternatively a perfect reflector has R = 1 which corresponds to negligible absorption η U CO η BH . In order to find the UCO viscosity dependent reflection coefficient, we follow the derivation given in [60] and extend their results for the inspiral phase where M ω 1. We consider the quadrupolar l = 2 perturbations, sourced by the external tidal field.…”

“…ξ, Θ are the bulk viscosity and the expansion, γ ab = h ab + u a u b is the projection metric and σ ab is the shear tensor. As demonstrated in [60] (for similar approach see [61]) by imposing the junction condition Eq. (2.6) on the UCO surface, we get a boundary condition that relates the UCO reflection coefficient to the membrane properties…”

Echoes from a singularity

“…The quasinormal modes (QNMs) are characterised by damped harmonic oscillations [47,48] that can also be excited by linear perturbation of the compact object. In general, QNMs of different compact objects will be different and can be used to distinguish ECOs from black holes [11,14,[49][50][51][52][53][54]. The horizon-less character of the ECOs may also be manifested by echoes in the ringdown profile [55][56][57][58][59][60][61][62][63].…”