Pseudospectrum and binary black hole merger transients

Abstract

The merger phase of binary black hole coalescences is a transient between an initial oscillating regime (inspiral) and a late exponentially damped phase (ringdown). In spite of the non-linear character of Einstein equations, the merger dynamics presents a surprisingly simple behaviour consistent with effective linearity. On the other hand, energy loss through the event horizon and by scattering to infinity renders the system non-conservative. Hence, the infinitesimal generator of the (effective) linear dynamics is a non-selfadjoint operator. Qualitative features of transients in linear dynamics driven by non-selfadjoint (in general, non-normal) operators are captured by the pseudospectrum of the time generator. We propose the pseudospectrum as a unifying framework to thread together the phases of binary black hole coalescences, from the inspiral-merger transition up to the late quasinormal mode ringdown.

Pseudospectrum of horizonless compact objects: A bootstrap instability mechanism

“…In the gravitational case, ref. [58] shows the absence of such early-time transient growth for asymptotically flat, spherically symmetric BH spacetimes. This result is independent of the specific underlying potential dictating the wave dynamics, and can be mathematically related to the fact that the field exits through the spacetime boundaries at the horizon and at infinity.…”

“…In particular, ref. [50], followed by [55][56][57][58], introduced the concept of pseudospectrum in the gravitational context, and first employed it to provide a systematic explanation of the lack of robustness of QNMs against small fluctuations of the underlying BH scattering potential, that were initially reported in refs. [59][60][61][62] (see also refs.…”

“…More recently, ref. [58] has further extended the range of applications of the pseudospectrum in the setting of GW physics. Specifically, whereas refs.…”

“…[50,[55][56][57] focus on the application of the pseudospectrum to the analysis of QNM spectral instabilities, ref. [58] rather addresses a set of genuinely dynamical phenomena, namely the possibility of transient growths in linear dynamics driven by non-selfadjoint operators, on the one hand, and the possibility of so-called pseudo-resonances, on the other hand. Indeed, while at late times the linear system dynamics is dominated by the decaying QNMs of the underlying evolution operator, its non-self-adjoint structure may lead to unexpected early-time transient growth that is neither related to non-linear effects nor to resonant-like responses of the system to external forcing (namely, socalled 'pseudo-resonances', in addition to actual proper resonant frequencies; see below), as observed in hydrodynamics [51,66,67].…”

“…Beyond dynamical transients, ref. [58] also emphasizes that the pseudospectrum framework provides an efficient tool to account for the resonant-like dynamical growth of perturbations when the non-self-adjoint linear system is acted upon by external forces. This fact is particularly relevant for the non-linear gravitational interaction, since the first order perturbation solution acts as a source for the second order dynamics [68].…”