Gravity seminar : Laura Sberna, University of Nottingham — Perturbation theory with black hole quasinormal modes

I will introduce a new method to study perturbations around black holes, using the black hole’s characteristic (quasinormal, quasibound or superradiant) modes. The new method hinges on a relativistic product, under which modes are orthogonal despite the non-self-adjoint nature of their equation. Using this product, one can derive the analog of time-dependent and independent perturbation theory in quantum mechanics. I will present a first application: the calculation of the self-gravitational frequency shift in a superradiant boson cloud, in closer agreement with numerical relativity than the non-relativistic “gravitational atom” approximation. The approach has many other practical applications, in gravitational-wave astronomy and beyond general relativity.