Chin. Phys. Lett.  2016, Vol. 33 Issue (03): 030401    DOI: 10.1088/0256-307X/33/3/030401
GENERAL |
Generalised Error Functions from the Kerr Metric
Wen-Lin Tang1,2, Zi-Ren Luo3,4, Yun-Kau Lau5**
1Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing Aerospace Control Center, Beijing 100094
2Department of Aerospace Guidance Navigation and Control, School of Astronautics, Beihang University, Beijing 100191
3QUEST Center of Quantum Engineering and Space-Time Research, Leibniz Universität Hannover, Hannover 30167, Germany
4Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Hannover 30167, Germany
5Institute of Applied Mathematics, Morningside Center of Mathematics and LESC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190
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Wen-Lin Tang, Zi-Ren Luo, Yun-Kau Lau 2016 Chin. Phys. Lett. 33 030401
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Abstract

Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special case of the fifth Painlevé transcendent is then worked out explicitly.

Received: 03 September 2015      Published: 31 March 2016
PACS:  04.20.-q (Classical general relativity)  
  04.70.Bw (Classical black holes)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/33/3/030401       OR      https://cpl.iphy.ac.cn/Y2016/V33/I03/030401
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Wen-Lin Tang
Zi-Ren Luo
Yun-Kau Lau
[1] Teukolsky S A 1973 Astrophys. J. 185 635
[2] Kerr R P 1963 Phys. Rev. Lett. 11 237
[3] Chandrasekhar S 1983 Math. Theory Black Holes 1st edn (Oxford: Clarendon Press)
[4] Leaver E W 1986 J. Math. Phys. 27 1238
[5] Finster F, Kamran N, Smoller J and Yau S T 2006 Commun. Math. Phys. 264 465
[6] Li L W, Kang X K and Leong M S 2004 Spheroidal Wave Functions in Electromagnetic Theory (New York: John Wiley & Sons)
[7] Simons F J 2010 Slepian Functions and Their Use in Signal Estimation and Spectral Analysis (Berlin: Springer) p 891
[8] Thompson W J 1999 Spheroidal Wave Functions, Computing in Science & Engineering p 84
[9] Madan L M 2006 Random Matrices (Beijing: Beijing World Publishing Corporation)
[10] Tian G H 2005 Chin. Phys. Lett. 22 3013
[11] Jimbo M, Miwa T, Môri Y and Sato M 1980 Physica D 1 80
[12] Andrews G E, Askey R A and Roy R 1993 Special Function (Cambridge: Cambridge University Press)
[13] Hua L K 2010 Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (Beijing: Science Press) (in Chinese)
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