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Black Hole Tomography: Unveiling Black Hole Ringdown via Gravitational Wave Observations

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Krishnan,  B.
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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2501.08964.pdf
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Citation

Metidieri, A. R., Bonga, B., & Krishnan, B. (in preparation). Black Hole Tomography: Unveiling Black Hole Ringdown via Gravitational Wave Observations.


Cite as: https://hdl.handle.net/21.11116/0000-0010-88EC-B
Abstract
During the post-merger regime of a binary black hole merger, the
gravitational wave signal consists of a superposition of quasi-normal modes
(QNMs) of the remnant black hole. It has been observed empirically, primarily
through numerical simulations and heuristic arguments, that the infalling
radiation at the horizon is also composed of a superposition of QNMs. In this
paper, we provide an analytic explanation for this observation in the
perturbative regime. Our analysis is based on a characteristic initial value
formulation where data is prescribed on the horizon (modeled as a perturbed
isolated horizon), and on a transversal null-hypersurface which registers the
outgoing radiation. This allows us to reformulate the traditional QNM problem
in a fully 4-dimensional setting. Using a mode-decomposition, we demonstrate
that the radiation modes crossing $\mathcal{H}$ are highly correlated with the
outgoing modes crossing $\mathcal{I}$, and provide explicit expressions linking
$\widetilde{\Psi}_0$ at the horizon with $\widetilde{\Psi}_4$ at null infinity.