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Separating metric perturbations in near-horizon extremal Kerr spacetimes

Chen, Baoyi and Stein, Leo C. (2017) Separating metric perturbations in near-horizon extremal Kerr spacetimes. Physical Review D, 96 (6). Art. No. 064017. ISSN 2470-0010. http://resolver.caltech.edu/CaltechAUTHORS:20170913-101951060

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Abstract

Linear perturbation theory is a powerful toolkit for studying black hole spacetimes. However, the perturbation equations are hard to solve unless we can use separation of variables. In the Kerr spacetime, metric perturbations do not separate, but curvature perturbations do. The cost of curvature perturbations is a very complicated metric-reconstruction procedure. This procedure can be avoided using a symmetry-adapted choice of basis functions in highly symmetric spacetimes, such as near-horizon extremal Kerr. In this paper, we focus on this spacetime and (i) construct the symmetry-adapted basis functions; (ii) show their orthogonality; and (iii) show that they lead to separation of variables of the scalar, Maxwell, and metric perturbation equations. This separation turns the system of partial differential equations into one of ordinary differential equations over a compact domain, the polar angle.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.96.064017DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.064017PublisherArticle
https://arxiv.org/abs/1707.05319arXivDiscussion Paper
Alternate Title:Separating metric perturbations in near-horizon extremal Kerr
Additional Information:© 2017 American Physical Society. Received 17 July 2017; published 13 September 2017. The authors would like to thank Yanbei Chen, Alex Lupsasca, Zachary Mark, and Peter Zimmerman for useful conversations. L. C. S. acknowledges the support of NSF Grant No. PHY–1404569, and both authors acknowledge the support of the Brinson Foundation. Some calculations used the computer algebra system mathematica, in combination with the xAct/xTensor suite [26,27].
Group:TAPIR
Funders:
Funding AgencyGrant Number
NSFPHY–1404569
Brinson FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20170913-101951060
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170913-101951060
Official Citation:Separating metric perturbations in near-horizon extremal Kerr spacetimes Baoyi Chen and Leo C. Stein Phys. Rev. D 96, 064017 – Published 13 September 2017
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81407
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Sep 2017 22:29
Last Modified:13 Sep 2017 22:29

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