The detection of gravitational waves necessitates high-precision models for the black hole post-merger phase, including non-linear effects.
In this talk, I will provide a complete treatment of linear and quadratic quasinormal modes (QNMs and QQNMs) in second-order perturbation theory, in Schwarzschild spacetime. We include novel methods for extracting QNMs and QQNMs amplitudes using a Laplace transform treatment, allowing for the inclusion of arbitrary initial data.
A key feature of this framework is the adoption of a hyperboloidal foliation, which permits the clean and efficient extraction of mode amplitudes at both the future null infinity and the black-hole horizon. Finally, we will discuss the impact of this framework on modeling the complete second-order ringdown.