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arXiv · 2310.05743

Mapping between black-hole perturbation theory and numerical relativity: gravitational-wave energy flux

Tousif Islam
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Abstract

We investigate the $α$-$β$ mapping, as previously introduced by Islam et al.~\cite{Islam:2022laz}, which relates numerical relativity (NR) and adiabatic point-particle black hole perturbation theory (BHPT) waveforms in the comparable mass regime for quasi-circular, non-spinning binary black holes. This mapping involves scaling the amplitude of individual modes with different values of $α$ and the time (and therefore the phase) with a single parameter, $β$. In this paper, we demonstrate that this scaling, both in terms of time and orbital frequencies, also extends to the overall gravitational-wave energy flux. This means that we can find a single $α_{\mathcal{F}}$ that scales the BHPT flux and a single $β_{\mathcal{F}}$ (which matches the value of $β$) that scales the BHPT time such a way that it aligns with NR flux evolution. We then explore the connection between the scaling parameter $α_{\mathcal{F}}$ ($β_{\mathcal{F}}$) and the missing finite size correction for the secondary black hole within the BHPT framework.

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Tousif Islam. 2023-10-09. Mapping between black-hole perturbation theory and numerical relativity: gravitational-wave energy flux. https://arxiv.org/abs/2310.05743

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