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 quasinormal 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 quasinormal 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 nonlinear 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 nonspinning 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.
Highlights
The process of binary black hole coalescence, the formation of a remnant black hole and the associated emission of gravitational waves, provides a rich arena for tests of general relativity (GR)
We have shown in this paper that the dynamics of the final apparent horizon in a binary black hole merger can be very well described by the quasinormal modes of the final black hole, from shortly after this horizon is formed onward
We have studied two quantities of interest, namely the shear of the outgoing normal at the horizon, and the horizon multipole moments; both of these are well modeled by quasinormal modes provided a large enough number of overtones is included
Summary
The process of binary black hole coalescence, the formation of a remnant black hole and the associated emission of gravitational waves, provides a rich arena for tests of general relativity (GR). A useful framework for tests of general relativity in this regime is provided by the parametrized post-Newtonian framework. It can be argued that it is the merger regime, which involves the formation of the remnant black hole and its approach to equilibrium, that is the most promising in the search for new physics. The approach of the remnant black hole to equilibrium is closely related to one of the important predictions of general relativity, namely the so-called black hole no-hair theorem (see e.g., [1,2,3] for reviews with diverse viewpoints). When the remnant black hole is initially formed, the spacetime in the vicinity of the horizon is highly dynamical and nonlinear, and it is responsible for the emitted gravitational radiation
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