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Abstract

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 is modeled as a perturbation around the final state.
The emitted gravitational waves will then be damped sinusoids with frequencies
and damping times given by the quasi-normal mode spectrum of the final 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 including the
higher overtones might hold even right after the remnant black hole is first
formed. At these times, the black hole is expected to be highly dynamical and
non-linear effects are likely to be important. 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 study the dynamics of the
final common horizon in terms of its shear and its multipole moments. We show
that they are indeed well described by a superposition of ringdown modes as
long as a sufficiently large number of higher overtones are included. This
description holds even for the highly dynamical final black hole shortly after
its formation. We discuss the implications and caveats of this result for black
hole spectroscopy and for our understanding of the approach to equilibrium.