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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. https://resolver.caltech.edu/CaltechAUTHORS:20150409-104722988

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## Abstract

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1088/0264-9381/32/6/065007DOIArticle
http://iopscience.iop.org/0264-9381/32/6/065007/PublisherArticle
http://arxiv.org/abs/1411.7297arXivDiscussion Paper
ORCID:
AuthorORCID
Lovelace, Geoffrey0000-0002-7084-1070
Giesler, Matthew0000-0003-2300-893X
Kidder, Lawrence E.0000-0001-5392-7342
Pfeiffer, Harald P.0000-0001-9288-519X
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSFPHY-1306125
NSFAST-1333129
NSFPHY-1440083
NSFAST-1333520
NSFPHY-1307489
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
NSFPHY-0960291
NSFTG-PHY990007N
NSFNSF-1429873
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150409-104722988
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
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:11 Apr 2015 00:42