Pseudospectrum and binary black hole merger transients

TL;DR

This paper introduces the pseudospectrum as a unifying framework to understand the transient dynamics of binary black hole mergers, bridging inspiral, merger, and ringdown phases despite the non-linear and non-conservative nature of Einstein's equations.

Contribution

It proposes using the pseudospectrum of the non-selfadjoint linearized operator to analyze and connect different phases of black hole coalescence transients.

Findings

Pseudospectrum captures qualitative features of black hole merger transients.

Framework unifies inspiral, merger, and ringdown phases.

Highlights the role of non-normal operators in gravitational wave dynamics.

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.