Asymptotics and Universality in Black Holes: from the quasinormal Weyl's law to the binary merger waveform
Current state-of-the-art approaches to black hole (BH) dynamics, encompassing several effective approximation schemes, offer a remarkable control of the quantitative aspects of strong gravity. They also provide key insights into some qualitative aspects of the problem. In spite of this, there remain blind spots that hinder the understanding of the mechanisms underlying some observed phenomena, in particular concerning simplicity and universality in BH spacetimes. Adopting an 'asymptotic reasoning' approach, by filtering non-essential degrees of freedom, can potentially unveil universality patterns by identifying key underlying structural stability mechanisms. We first illustrate such an asymptotic approach by focusing on a BH quasinormal (QNM) Weyl's law, that accounts for the universal asymptotics of the QNM "counting function". This permits to identify light-trapping and the (local) redshift effect as the underlying mechanisms, also offering a bridge to the universal patterns found in BH QNM spectral instability. As a by-product, Weyl's law universality formally opens an observational access to spacetime (effective) dimensionality. More heuristically, we sketch a program recently put forward to apply such 'asymptotic reasoning' to address the observed simplicity and universality patterns in binary BH merger dynamics. This program is built as a hierarchy of asymptotic models, potentially making contact with integrability theory in gravity, namely through the background sector in a "wave-mean flow" approach to BH binary dynamics.