arXiv subjects

Corentin Vitel

Publications and source records attributed to Corentin Vitel.

3 recordsLinked to original sources

arXiv2026

Integrability in Asymptotic Symmetries of Spacetime: the $\text{BMS}_3$ scenario

We revisit the proof of a $\mathfrak{bms}_3-$integrable hierarchy introduced in Fuentealba et al. (JHEP, 2018), using different structural methodologies. Specifically, from the variational complex on the ring of polynomial symbols, a $\mathfrak{bms}_3$ bi-Hamiltonian structure is constructed on which a Nijenhuis operator can be attached. A similar argument is made for the $\mathrm{AdS}_3$ case, where we check that the flat limit of the latter recovers the asymptotically flat situation. An alternative $\tau-$scheme description is also presented. Moreover, a Lie-Poisson description suggests that such a $\mathfrak{bms}_3-$hierarchy is not unique. For a subclass of so-called energy-dependent Schr\"odinger operators, it is shown that their Lax flows are described by the coadjoint orbits of $\mathfrak{bms}_3$.

math-ph↗

arXiv2025

Black Hole Scattering and Integrability: A Hyperboloidal Approach

Integrability structures are known to play a key role in one-dimensional scattering. In the Schwarzschild gravitational context, the analysis emphasizing the role of the so-called Darboux covariance and its intimate connection with KdV conserved quantities was recently introduced by Lenzi & Sopuerta. In a second stage, together with Jaramillo, this led in particular to the identification of the structural role of the "KdV-Virasoro-Schwarzian derivative" triangle in this problem. Such a gravitational scattering description dwells naturally on a Cauchy foliation of the spacetime. In the following, we first review--for the Schwarzschild background--this problem in a hyperboloidal foliation scheme, where the infinitesimal time generator of the dynamics is a non-selfadjoint operator. Then, we explore the underlying integrability features through a Lax-pair formulation. Specifically, the main results presented here are i) the explicit proposal of a weak Lax-pair, valid under suitable conditions involving fields at null infinity, with ii) the construction of the associated infinite sequence of isospectral flows. From a broader perspective, the very form of the non-selfadjoint infinitesimal time operator, which neatly separates into two components corresponding to bulk and boundary structures, paves the way for the description of the gravitational dynamics in terms of a "semi-direct action" of bulk degrees of freedom onto boundary degrees of freedom. This is akin to the "wave-mean flow" approach for black hole strong-gravity dynamics recently proposed in this line of research.

gr-qc↗

arXiv2025

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.

gr-qc↗