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

• Published in: arXiv.org 2021-09
• Main Authors: Dhesi, Mekhi, Rüter, Hannes R, Pound, Adam, Barack, Leor, Pfeiffer, Harald P
• Format: Article
• Language: English
• Subjects: Black holes; Finite difference method; Mass ratios; Matching; Mathematical models; Simulation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2109.03531

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.