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Momentum flow in black-hole binaries. II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins

Lovelace, Geoffrey and Chen, Yanbei and Cohen, Michael and Kaplan, Jeffrey D. and Keppel, Drew and Matthews, Keith D. and Nichols, David A. and Scheel, Mark A. and Sperhake, Ulrich (2010) Momentum flow in black-hole binaries. II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins. Physical Review D, 82 (6). Art. No. 064031. ISSN 2470-0010.

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Research on extracting science from binary-black-hole (BBH) simulations has often adopted a “scattering matrix” perspective: given the binary’s initial parameters, what are the final hole’s parameters and the emitted gravitational waveform? In contrast, we are using BBH simulations to explore the nonlinear dynamics of curved spacetime. Focusing on the head-on plunge, merger, and ringdown of a BBH with transverse, antiparallel spins, we explore numerically the momentum flow between the holes and the surrounding spacetime. We use the Landau-Lifshitz field-theory-in-flat-spacetime formulation of general relativity to define and compute the density of field energy and field momentum outside horizons and the energy and momentum contained within horizons, and we define the effective velocity of each apparent and event horizon as the ratio of its enclosed momentum to its enclosed mass-energy. We find surprisingly good agreement between the horizons’ effective and coordinate velocities. During the plunge, the holes experience a frame-dragging-induced acceleration orthogonal to the plane of their spins and their infall (“downward”), and they reach downward speeds of order 1000  km/s. When the common apparent horizon forms (and when the event horizons merge and their merged neck expands), the horizon swallows upward field momentum that resided between the holes, causing the merged hole to accelerate in the opposite (“upward”) direction. As the merged hole and the field energy and momentum settle down, a pulsational burst of gravitational waves is emitted, and the merged hole has a final effective velocity of about 20  km/s upward, which agrees with the recoil velocity obtained by measuring the linear momentum carried to infinity by the emitted gravitational radiation. To investigate the gauge dependence of our results, we compare generalized harmonic and Baumgarte-Shapiro-Shibata-Nakamura-moving-puncture evolutions of physically similar initial data; although the generalized harmonic and Baumgarte-Shapiro-Shibata-Nakamura-moving-puncture simulations use different gauge conditions, we find remarkably good agreement for our results in these two cases. We also compare our simulations with the post-Newtonian trajectories and near-field energy-momentum.

Item Type:Article
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URLURL TypeDescription
Lovelace, Geoffrey0000-0002-7084-1070
Chen, Yanbei0000-0002-9730-9463
Sperhake, Ulrich0000-0002-3134-7088
Additional Information:© 2010 The American Physical Society. Received 4 July 2009; published 24 September 2010. We are pleased to acknowledge Michael Boyle, Jeandrew Brink, Lawrence Kidder, Robert Owen, Harald Pfeiffer, Saul Teukolsky, and Kip Thorne for helpful discussions. This work was supported in part by the Sherman Fairchild Foundation, the Brinson Foundation, the David and Barbara Groce Fund at Caltech, NSF Grants No. PHY-0652952, No. DMS-0553677, No. PHY-0652929, No. PHY-0601459, No. PHY-0652995, No. PHY-0653653, No. DMS-0553302, and NASA Grants No. NNX09AF96G and No. NNX09AF97G. Some calculations were done on the Ranger cluster under NSF TeraGrid Grant No. PHY-090003.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
Caltech David and Barbara Groce FundUNSPECIFIED
Issue or Number:6
Classification Code:PACS; 04.25.D-, 04.25.dg, 04.25.Nx, 04.70.-s
Record Number:CaltechAUTHORS:20101026-080417399
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20521
Deposited By: Tony Diaz
Deposited On:24 Nov 2010 22:32
Last Modified:09 Mar 2020 13:19

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