Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field model in 3 + 1 dimensions
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1.
California Institute of Technology
Abstract
Binary black hole simulations become increasingly more computationally expensive with smaller mass ratios, partly because of the longer evolution time, and partly because the lengthscale disparity dictates smaller time steps. The program initiated by Dhesi et al. [Phys. Rev. D 104, 124002 (2021)] explores a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range (10⁻⁴ ≲ q ≲ 10⁻²), where purely perturbative methods may not be adequate. A region ("worldtube") much larger than the small black hole is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. Here we apply this idea to a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field. This is a first implementation of the worldtube excision method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of the method, and discuss the steps toward applying it for evolving orbits and, ultimately, in the binary black-hole scenario. Our implementation is publicly accessible in the spectre numerical relativity code.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Open access publication funded by the Max Planck Society.
Acknowledgement
We thank Benjamin Leather for computing a reference value of the angular derivative of the regular field at the particle position. This work was supported in part by the Sherman Fairchild Foundation and by NSF Grants No. PHY-2011961, No. PHY-2011968, and No. OAC-1931266 at Caltech, by NSF Grants No. PHY-1912081 and No. OAC-1931280 at Cornell, and by NSF Grants No. PHY-1654359 and No. PHY-2208014 at Cal State Fullerton. A. P. acknowledges the support of a Royal Society University Research Fellowship. P. K.'s research was supported by the Department of Atomic Energy, Government of India; and by the Ashok and Gita Vaish Early Career Faculty Fellowship at the International Centre for Theoretical Sciences. H. R. R. acknowledges support from the Fundação para a Ciência e Tecnologia (FCT) within the projects UID/04564/2021, UIDB/04564/2020, UIDP/04564/2020 and EXPL/FIS-AST/0735/2021. spectre uses charm++/converse [63,64], which was developed by the Parallel Programming Laboratory in the Department of Computer Science at the University of Illinois at Urbana-Champaign. spectre uses blaze [65,66], hdf5 [67], the GNU Scientific Library (gsl) [68], yaml-cpp [69], pybind11 [70], libsharp [71], and libxsmm [72]. The figures in this article were produced with matplotlib [73,74], numpy [75], and paraview [76,77]. The authors thank Charlie Vu for helpful discussions.
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Additional details
- ISSN
- 2470-0029
- Sherman Fairchild Foundation
- PHY-2011961
- National Science Foundation
- PHY-2011968
- National Science Foundation
- OAC-1931266
- National Science Foundation
- PHY-1912081
- National Science Foundation
- OAC-1931280
- National Science Foundation
- PHY-1654359
- National Science Foundation
- PHY-2208014
- National Science Foundation
- Royal Society
- Department of Atomic Energy
- UID/04564/2021
- Fundação para a Ciência e Tecnologia
- UIDB/04564/2020
- Fundação para a Ciência e Tecnologia
- UIDP/04564/2020
- Fundação para a Ciência e Tecnologia
- EXPL/FIS-AST/0735/2021
- Fundação para a Ciência e Tecnologia
- Max Planck Society
- Caltech groups
- TAPIR, Walter Burke Institute for Theoretical Physics