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Tidal response and near-horizon boundary conditions for spinning exotic compact objects

Chen, Baoyi and Wang, Qingwen and Chen, Yanbei (2021) Tidal response and near-horizon boundary conditions for spinning exotic compact objects. Physical Review D, 103 (10). Art. No. 104054. ISSN 2470-0010. doi:10.1103/physrevd.103.104054.

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Teukolsky equations for |s| = 2 provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an ingoing (outgoing) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the membrane paradigm, by considering a family of zero-angular-momentum fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to ingoing gravitational waves, respond to these waves, and generate outgoing waves. As it also turns out, if both ingoing and outgoing waves exist near the horizon, the Newman-Penrose (NP) quantity ψ₀ will be numerically dominated by the ingoing wave, while the NP quantity ψ₄ will be dominated by the outgoing wave—even though both quantities contain full information regarding the wave field. In this way, we obtain the ECO boundary condition in the form of a relation between ψ₀ and the complex conjugate of ψ₄, in a way that is determined by the ECO’s tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame and deduce the corresponding ECO boundary condition for Teukolsky functions. Using the Starobinsky-Teukolsky identity, we subsequently obtain the boundary condition for ψ₄ alone, as well as for the Sasaki-Nakamura and Detweiler functions. As it also turns out, the reflection of spinning ECOs will generically mix between different ℓ components of the perturbation fields, and it will be different for perturbations with different parities. It is straightforward to apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and to solve for the spinning ECOs’ quasinormal modes.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Chen, Baoyi0000-0002-3927-6843
Chen, Yanbei0000-0002-9730-9463
Additional Information:© 2021 American Physical Society. (Received 1 January 2021; accepted 28 April 2021; published 25 May 2021) The authors would like to thank Shuo Xin, Wenbiao Han, Ka-Lok R. Lo, Ling Sun, and Niayesh Afshordi for useful conversations. B. C. and Y. C. acknowledge the support from the Brinson Foundation, the Simons Foundation (Grant No. 568762), and the National Science Foundation, Grants No. PHY-2011961 and No. PHY-2011968. Q. W. acknowledges the support from the University of Waterloo, Natural Sciences and Engineering Research Council of Canada (NSERC), and the Perimeter Institute for Theoretical Physics.
Group:TAPIR, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Brinson FoundationUNSPECIFIED
Simons Foundation568762
University of WaterlooUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20210527-093457434
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109278
Deposited By: George Porter
Deposited On:27 May 2021 17:43
Last Modified:27 May 2021 22:34

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