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Scalar Green function of the Kerr spacetime

Yang, Huan and Zhang, Fan and Zimmerman, Aaron and Chen, Yanbei (2014) Scalar Green function of the Kerr spacetime. Physical Review D, 89 (6). Art. No. 064014. ISSN 2470-0010.

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In this paper we study the scalar Green function in the Kerr spacetime using Wentzel-Kramers-Brillouin (WKB) methods. The Green function can be expressed by Fourier-transforming to its frequency-domain counterpart, and with the help of complex analysis it can be divided into parts: 1) the “direct part,” which propagates on the light cone and dominates at very early times; 2) the “quasinormal-mode part,” which represents the waves traveling around the photon sphere and is important at early and intermediate times; and 3) the “tail part,” which is due to scattering by the Coulomb-type potential and becomes more important at later times. We focus on the “quasinormal-mode part” of the Green function and derive an approximate analytical formula for it using WKB techniques. This approximate Green function diverges at points that are connected by null geodesics, and it recovers the fourfold singular structure of Green functions that are seen in Schwarzschild and other spacetimes. It also carries unique signatures of the Kerr spacetime such as frame dragging. Along the way, we also derive approximate quasinormal-mode wave functions and expressions for the black hole excitation factors in the Kerr spacetime. We expect this work to benefit the understanding of both wave propagation and the problem of self-force in the Kerr spacetime.

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Additional Information:© 2014 American Physical Society. Published 6 March 2014; Received 15 November 2013. We thank Marc Casals and Sam Dolan for helpful discussions on the Schwarzschild Green function, and Anıl Zenginoğlu on the numerical Kerr Green function. We also would like to thank Marc Casals for his advice on an early draft of this paper. This research is funded by NSF Grants No. PHY-1068881 and No. PHY-1005655, CAREER Grants No. PHY-0956189 and No. PHY- 1055103, NASA Grant No. NNX09AF97G, the Sherman Fairchild Foundation, the Brinson Foundation, and the David and Barbara Groce Startup Fund at Caltech. H. Y. acknowledges supports from the Perimeter Institute of Theoretical Physics and the Institute for Quantum Computing. Research at Perimeter Institute is supported by the government of Canada and by the province of Ontario though Ministry of Research and Innovation.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
David and Barbara Groce Startup FundUNSPECIFIED
Perimeter Institute of Theoretical PhysicsUNSPECIFIED
Institute for Quantum ComputingUNSPECIFIED
Issue or Number:6
Classification Code:PACS: 04.30.-w, 04.25.Nx, 04.30.Nk
Record Number:CaltechAUTHORS:20140424-093700933
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Official Citation:Yang, H., Zhang, F., Zimmerman, A., & Chen, Y. (2014). Scalar Green function of the Kerr spacetime. Physical Review D, 89(6), 064014.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45186
Deposited By: Jason Perez
Deposited On:24 Apr 2014 17:12
Last Modified:03 Oct 2019 06:27

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