Where is the ringdown? Reconstructing quasinormal modes from dispersive waves

We study the generation and propagation of gravitational waves in scalar-tensor gravity using numerical relativity simulations of scalar field collapses beyond spherical symmetry. This allows us to compare the tensor and additional massive scalar waves that are excited. As shown in previous work in spherical symmetry, massive propagating scalar waves decay faster than 1/r and disperse, resulting in an inverse chirp. These effects obscure the ringdown in any extracted signal by mixing it with the transient responses of the collapse during propagation. In this paper we present a simple method to rewind the extracted signals to horizon formation, which allows us to clearly identify the ringdown phase and extract the amplitudes of the scalar quasinormal modes, quantifying their excitation in strong gravity events and verifying the frequencies to perturbative calculations. The effects studied are relevant to any theories in which the propagating waves have a dispersion relation, including the tensor case.