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Black hole ringdown spectroscopy and higher overtones
It is expected that all astrophysical black holes in equilibrium are well described by the Kerr solution. Moreover, any black hole far away from equilibrium, such as one initially formed in a compact binary merger or by the collapse of a massive star, will eventually reach a final equilibrium Kerr state. At sufficiently late times in this process of reaching equilibrium, we expect that the black hole can be modelled as a perturbed Kerr black hole and the emitted gravitational waves will be damped sinusoids with frequencies and damping times given by the quasi-normal modes of the corresponding Kerr black hole. An observational test of this scenario, often referred to as black hole spectroscopy, is one of the major goals of gravitational wave astronomy. It was recently suggested that the quasi-normal mode description might hold well into what should be the non-perturbative regime, namely even right after the remnant black hole is first formed. In this paper we investigate this remarkable scenario in terms of the horizon dynamics. Working with high accuracy simulations of a simple configuration, namely the head-on collision of two non-spinning black holes with unequal masses, we show that the dynamics of the final black hole horizon is indeed well described by a superposition of ringdown modes as long as the higher overtones are included. We show that this description holds even for the highly dynamical final black hole shortly after its formation. We demonstrate that the time dependence of the shear of the common horizon and its multipole moments can be accurately represented by a superposition of quasi-normal modes if a sufficiently large number of overtones are used for the data modelling. We discuss the implications and caveats of this result for black hole spectroscopy and for our understanding of the approach to equilibrium.