Excitation And Fitting Of A Ringing Black Hole

The lack of a set of basis functions complicates black hole ringdown analysis. While one can fit the ringdown signal from a binary black hole merger to high precision using a set of damped sinusoids even before the peak strain, the initial transient, non-modal contents, and nonlinear effects put one susceptible to over-fitting. In this talk, we present a novel way of extracting the overtone contents from a single perturbed black hole, using spatial eigenfunctions for the quasinormal modes on a compactified hyperboloidal slicing. We show that when fitting the signal in both space and time, the set of functions constructed from quasinormal eigenfunctions becomes orthogonal under a simple bilinear form; present a simple way of numerically calculating the excitation amplitudes for the quasinormal modes on the hyperboloidal slice from initial data; show that one can distinguish the modal and non-modal contributions in the signal; and lastly, how nonlinear effects may affect the fitting.