Black hole tomography: Unveiling black hole horizon dynamics via ringdown observations

Abstract

During the post-merger regime of a binary black hole merger, thegravitational wave signal consists of a superposition of quasi-normal modes(QNMs) of the remnant black hole. It has been observed empirically, primarilythrough numerical simulations and heuristic arguments, that the infallingradiation at the horizon is also composed of a superposition of QNMs. In thispaper, we provide an analytic explanation for this observation in theperturbative regime. Our analysis is based on a characteristic initial valueformulation where data is prescribed on the horizon (modeled as a perturbedisolated horizon), and on a transversal null-hypersurface which registers theoutgoing radiation. This allows us to reformulate the traditional QNM problemin a fully 4-dimensional setting. Using a mode-decomposition, we demonstratethat the radiation modes crossing $\mathcal{H}$ are highly correlated with theoutgoing modes crossing $\mathcal{I}$, and provide explicit expressions linking$\widetilde{\Psi}_0$ at the horizon with $\widetilde{\Psi}_4$ at null infinity.<br