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Nearly extremal apparent horizons in simulations of merging black holes

Lovelace, Geoffrey and Scheel, Mark A. and Owen, Robert and Giesler, Matthew and Katebi, Reza and Szilágyi, Béla and Chu, Tony and Demos, Nicholas and Hemberger, Daniel A. and Kidder, Lawrence E. and Pfeiffer, Harald P. and Afshari, Nousha (2015) Nearly extremal apparent horizons in simulations of merging black holes. Classical and Quantum Gravity, 32 (6). Art. No. 065007. ISSN 0264-9381.

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The spin angular momentum S of an isolated Kerr black hole is bounded by the surface area A of its apparent horizon: 8πS ≤ A, with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses M and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to S/M^2 = 0.994. We measure the area and (using approximate Killing vectors) the spin on the individual and common apparent horizons, finding that the inequality 8πS < A is satisfied in all cases but is very close to equality on the common apparent horizon at the instant it first appears. We also evaluate the Booth–Fairhurst extremality, whose value for a given apparent horizon depends on the scaling of the horizon's null normal vectors. In particular, we introduce a gauge-invariant lower bound on the extremality by computing the smallest value that Booth and Fairhurst's extremality parameter can take for any scaling. Using this lower bound, we conclude that the common horizons are at least moderately close to extremal just after they appear. Finally, following Lovelace et al (2008 Phys. Rev. D 78 084017), we construct quasiequilibrium binary-black hole initial data with 'overspun' marginally trapped surfaces with $8\pi S\gt A$. We show that the overspun surfaces are indeed superextremal: our lower bound on their Booth–Fairhurst extremality exceeds unity. However, we confirm that these superextremal surfaces are always surrounded by marginally outer trapped surfaces (i.e., by apparent horizons) with $8\pi S\lt A$. The extremality lower bound on the enclosing apparent horizon is always less than unity but can exceed the value for an extremal Kerr black hole.

Item Type:Article
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URLURL TypeDescription Paper
Lovelace, Geoffrey0000-0002-7084-1070
Giesler, Matthew0000-0003-2300-893X
Kidder, Lawrence E.0000-0001-5392-7342
Pfeiffer, Harald P.0000-0001-9288-519X
Additional Information:© IOP Publishing Ltd. Received 26 November 2014; Accepted for publication 7 January 2015; Published 26 February 2015. We are pleased to thank Sergio Dain for the original inspiration for this work through his presentation at GR20, Kevin Kuper for assisting in formatting some figures, and Christian Ott, Saul Teukolsky, and Evan Foley for helpful discussions. Simulations used in this work were computed with SpEC [42]. Figures were prepared and some calculations were performed using Mathematica. This work was supported in part by the Sherman Fairchild Foundation; NSF grants PHY-1306125 and AST-1333129 at Cornell, NSF grants PHY-1440083 and AST-1333520 at Caltech, and NSF grant PHY-1307489 at California State University Fullerton; a 2013–2014 California State University Fullerton Junior Faculty Research Grant; and NSERC of Canada, the Canada Chairs Program, and the Canadian Institute for Advanced Research. Computations were performed on the Zwicky cluster at Caltech, which is supported by the Sherman Fairchild Foundation and by NSF award PHY-0960291; on the NSF XSEDE network under grant TG-PHY990007N; on the Orca cluster supported by NSF award NSF-1429873, by the Research Corporation for Science Advancement, and by California State University Fullerton; and on the GPC supercomputer at the SciNet HPC Consortium [80]. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund–Research Excellence; and the University of Toronto.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Canada Chairs ProgramUNSPECIFIED
Canadian Institute for Advanced Research (CIAR)UNSPECIFIED
Research Corporation for Science AdvancementUNSPECIFIED
California State University Fullerton (CSUF)UNSPECIFIED
Canada Foundation for InnovationUNSPECIFIED
Government of OntarioUNSPECIFIED
Ontario Research Fund–Research ExcellenceUNSPECIFIED
University of TorontoUNSPECIFIED
Issue or Number:6
Record Number:CaltechAUTHORS:20150409-104722988
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Official Citation:Nearly extremal apparent horizons in simulations of merging black holes Geoffrey Lovelace et al 2015 Class. Quantum Grav. 32 065007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56528
Deposited By: Jason Perez
Deposited On:11 Apr 2015 00:42
Last Modified:09 Mar 2020 13:19

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