Painlev\'e-II approach to binary black hole merger dynamics: universality from integrability

Understand

The binary black hole merger waveform is both simple and universal.

• Adopting an effective asymptotic description of the dynamics, we aim at accounting for such universality in terms of underlying (effective) integrable structures.
• More specifically, under a ``wave-mean flow'' perspective, we propose that fast degrees of freedom corresponding to the observed waveform would be subject to effective linear dynamics, propagating on a slowly evolving background subject to (effective) non-linear integrable dynamics.
• The Painlev\'e property of the latter would be implemented in terms of the so-called Painlev\'e-II transcendent, providing a structural link between i) orbital (in particular, EMRI) dynamics in the inspiral phase, ii) self-similar solutions of non-linear dispersive Korteweg-de Vries-like equations (namely, the `modified Korteweg-de Vries' equation) through the merger and iii) the matching with the isospectral features of black hole quasi-normal modes in late ringdown dynamics.