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Binary-black-hole initial data with nearly extremal spins

Lovelace, Geoffrey and Owen, Robert and Pfeiffer, Harald P. and Chu, Tony (2008) Binary-black-hole initial data with nearly extremal spins. Physical Review D, 78 (8). Art. No. 084017. ISSN 0556-2821.

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There is a significant possibility that astrophysical black holes with nearly extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing binary-black-hole initial data, focusing on their ability to generate black holes with nearly extremal spins: (i) Bowen-York initial data, including standard puncture data (based on conformal flatness and Bowen-York extrinsic curvature), (ii) standard quasiequilibrium initial data (based on the extended-conformal-thin-sandwich equations, conformal flatness, and maximal slicing), and (iii) quasiequilibrium data based on the superposition of Kerr-Schild metrics. We find that the two conformally flat methods (i) and (ii) perform similarly, with spins up to about 0.99 obtainable at the initial time. However, in an evolution, we expect the spin to quickly relax to a significantly smaller value around 0.93 as the initial geometry relaxes. For quasiequilibrium superposed Kerr-Schild data [method (iii)], we construct initial data with initial spins as large as 0.9997. We evolve superposed Kerr-Schild data sets with spins of 0.93 and 0.97 and find that the spin drops by only a few parts in 10^4 during the initial relaxation; therefore, we expect that superposed Kerr-Schild initial data will allow evolutions of binary black holes with relaxed spins above 0.99. Along the way to these conclusions, we also present several secondary results: the power-law coefficients with which the spin of puncture initial data approaches its maximal possible value; approximate analytic solutions for large spin puncture data; embedding diagrams for single spinning black holes in methods (i) and (ii); nonunique solutions for method (ii). All of the initial-data sets that we construct contain subextremal black holes, and when we are able to push the spin of the excision boundary surface into the superextremal regime, the excision surface is always enclosed by a second, subextremal apparent horizon. The quasilocal spin is measured by using approximate rotational Killing vectors, and the spin is also inferred from the extrema of the intrinsic scalar curvature of the apparent horizon. Both approaches are found to give consistent results, with the approximate-Killing-vector spin showing the least variation during the initial relaxation.

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Additional Information:© 2008 The American Physical Society. (Received 27 May 2008; published 10 October 2008) It is a pleasure to acknowledge useful discussions with Ivan Booth, Gregory Cook, Stephen Fairhurst, Lawrence Kidder, Lee Lindblom, Mark Scheel, Saul Teukolsky, and Kip Thorne. The numerical calculations in this paper were performed using the Spectral Einstein Code (SpEC), which was primarily developed by Lawrence Kidder, Harald Pfeiffer, and Mark Scheel. We would also like to acknowledge the anonymous referee for reminding us of an important technical caveat. Some equations in this paper were obtained using MATHEMATICA. This work was supported in part by grants from the Sherman Fairchild Foundation to Caltech and Cornell and from the Brinson Foundation to Caltech; by NSF Grants No. PHY-0652952, No. DMS-0553677, and No. PHY-0652929 and NASA Grant No. NNG05GG51G at Cornell; and by NSF Grants No. PHY-0601459, No. PHY-0652995, and No. DMS-0553302 and NASA Grant No. NNG05GG52G at Caltech.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
National Science FoundationPHY-0652952
National Science FoundationDMS-0553677
National Science FoundationPHY-0652929
National Science FoundationPHY-0601459
National Science FoundationPHY-0652995
National Science FoundationDMS-0553302
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ID Code:11935
Deposited By: Archive Administrator
Deposited On:11 Oct 2008 05:40
Last Modified:26 Dec 2012 10:24

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