Séminaire Amplitudes et Gravitation sur l'Yvette (IHES/IPhT)
Reconstructing the metric of a perturbed black hole due to the presence of a companion, including both the stationary and radiative contributions, is a highly non-trivial problem. In this talk, we address this to linear order in perturbation theory through the characteristic initial value formulation, prescribing data on two intersecting null hypersurfaces, one of which is a perturbed isolated horizon. By including the possibility of small amounts of infalling radiation at the horizon, we show that the ringdown modes arise naturally in this formalism when there is no incoming radiation from null infinity. This therefore establishes analytically strong correlations between the usual quasi-normal modes observed in the outgoing radiation with the horizon geometry and the infalling radiation at the horizon. This can be viewed as a demonstration of black hole tomography in a perturbative setting, where we are able to determine the detailed dynamics of the horizon geometry based on observations of gravitational waves from the late stage of a binary black hole merger.
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Julio Parra-Martinez & Alessandro Podo
