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Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model

Dhesi, M., Rüter, H. R., Pound, A., Barack, L., & Pfeiffer, H. (2021). Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model. Physical Review D, 104 (12 ): 124002. doi:10.1103/PhysRevD.104.124002.

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Dhesi, Mekhi, Author
Rüter, Hannes R.1, Author
Pound, Adam, Author
Barack, Leor, Author
Pfeiffer, Harald1, Author
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1Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1933290

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Free keywords: General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE
Abstract: The computational cost of inspiral and merger simulations for black-hole binaries increases in inverse proportion to the square of the mass ratio $q:=m_2/m_1\leq 1$. One factor of $q$ comes from the number of orbital cycles, which is proportional to $1/q$, and another is associated with the required number of time steps per orbit, constrained (via the Courant-Friedrich-Lewy condition) by the need to resolve the two disparate length scales. This problematic scaling makes simulations progressively less tractable at smaller $q$. Here we propose and explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q\lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region of radius much larger than $m_2$ around the smaller object is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. The analytical model involves certain a priori unknown parameters, associated with unknown bits of physics together with gauge-adjustment terms; these are dynamically determined by matching to the numerical solution outside the excision region. In this paper we develop the basic idea and apply it to a toy model of a scalar charge in a circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in a 1+1D framework. Our main goal here is to explore the utility and properties of different matching strategies, and to this end we develop two independent implementations, a finite-difference one and a spectral one. We discuss the extension of our method to a full 3D numerical evolution and to gravity.

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Dates: 2021-09-082021
Publication Status: Published in print
Pages: 24 pages, 18 figures
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Identifiers: arXiv: 2109.03531
DOI: 10.1103/PhysRevD.104.124002
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Title: Physical Review D
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Pages: - Volume / Issue: 104 (12 ) Sequence Number: 124002 Start / End Page: - Identifier: -