A binary black hole metric approximation from inspiral to merger

Luciano Combi; Sean M. Ressler

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arXiv · 2403.13308

A binary black hole metric approximation from inspiral to merger

Luciano Combi·Sean M. Ressler

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Abstract

We present a semi-analytical binary black hole (BBH) metric approximation that models the entire evolution of the system from inspiral to merger. The metric is constructed as a boosted Kerr-Schild superposition following post-Newtonian (PN) trajectories at the fourth PN order in the inspiral phase. During merger, we interpolate the binary metric in time to a single black hole remnant with properties obtained from numerical relativity (NR) fitting formulas. The new metric can model binary black holes with arbitrary spin direction, mass ratio, and eccentricity at any stage of their evolution in a fast and computationally efficient way. We analyze the properties of our new metric and compare it with a full numerical relativity evolution. Hamiltonian constraints are well-behaved even at merger, and the mass and spin measured self-consistently on the black hole's apparent horizon deviate on average by only $\lesssim 10 \%$ compared to the full numerical evolution. We perform General Relativistic Magneto-hydrodynamical (GRMHD) simulations for two cases: merging black holes in a uniform gas, and inspiralling black holes accreting from a magnetized circumbinary disk. We demonstrate that, in both cases, the properties of the gas, such as the accretion rate, are remarkably similar between the two approaches, with small average differences. We demonstrate that our approximate metric significantly reduces computational costs compared to full numerical relativity, enabling a new class of high-resolution, long-term binary accretion simulations. The numerical implementation of the metric is now open-source and optimized for numerical work.

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Luciano Combi, Sean M. Ressler. 2026-01-18. A binary black hole metric approximation from inspiral to merger. https://arxiv.org/abs/2403.13308

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