Speaker
Description
Black Hole Perturbation Theory (BHPT) has been shown to be very successful in describing physical processes around BHs. In particular, the scattering of electromagnetic and gravitational waves (and other physical fields) and the so-called quasinormal mode (QNM) oscillations, the damped BH oscillations that dominate the ringdown phase of binary BH (BBH) coalescences.
A key feature of BHPT is that all the physically observable quantities can be obtained only in terms of (gauge-invariant) master functions that decouple the perturbative Einstein equations. In this talk, I will argue that, in the Schwarzschild case, this fact is connected to an underlying Darboux covariance structure of the space of master functions and equations.
Beyond this, one can deform the time-independent Schroedinger-type master equations along the flow of the completely integrable Korteweg–de Vries (KdV) hierarchy. This integrable structure generates an infinite tower of conserved quantities, the KdV integrals, which fully determine scattering amplitudes through a classical moment problem. In this way, integrability provides a new organizing principle for the perturbative dynamics of BHs.
Finally, I will discuss the additional integrability structures that appear and the important role that they can play in getting a deeper understanding of the general dynamics of BHs and what are the prospects of using these methods in the BBH problem.
