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Explore black hole tomography through a mathematical physics lecture that demonstrates how to reconstruct the metric of perturbed black holes using characteristic initial value formulation. Learn about the complex problem of determining black hole geometry when influenced by a companion object, including both stationary and radiative contributions addressed through linear perturbation theory. Discover how prescribing data on two intersecting null hypersurfaces—one being a perturbed isolated horizon—enables the reconstruction process. Examine how small amounts of infalling radiation at the horizon naturally give rise to ringdown modes when no incoming radiation exists from null infinity. Understand the analytical correlations established between quasi-normal modes observed in outgoing radiation and both horizon geometry and infalling radiation at the horizon. Gain insights into this perturbative demonstration of black hole tomography, which enables determination of detailed horizon geometry dynamics based on gravitational wave observations from late-stage binary black hole mergers.
