Abstract
The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino (s=1/2), electromagnetic (s=1), Rarita-Schwinger (s=3/2), and gravitational (s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun’s equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.
Similar content being viewed by others
References
Blandin, J., Pons, R., Marcilhacy, G.: Lett. Nuovo Cimento 39(17), 561 (1983)
Carmeli, M.: Classical Fields: General Relativity and Gauge Theory. Wiley, New York (1982)
Carter, B.: Commun. Math. Phys. 10(4), 280 (1968)
Chruściel, P.T., Ölz, C.R., Szybka, S.J.: Phys. Rev. D, Part. Fields 86(12), 124041 (2012)
Fackerell, E.D., Crossman, R.G.: J. Math. Phys. 18(9), 1849 (1977)
Gibbons, G.W., Hawking, S.W.: Phys. Rev. D, Part. Fields 15(10), 2738 (1977)
Goldberg, J.N., Sachs, R.K.: Acta Phys. Pol. B, Proc. Suppl. 22, 13 (1962)
Goldberg, J.N., Macfarlane, A.J., Newman, E.T., Rohrlich, F., Sudarshan, E.C.G.: J. Math. Phys. 8(11), 2155 (1967)
Konoplya, R.A., Zhidenko, A.: Phys. Rev. D, Part. Fields 76(8), 084018 (2007)
Konoplya, R.A., Zhidenko, A.: Rev. Mod. Phys. 83(3), 793 (2011)
Leaver, E.W.: J. Math. Phys. 27(5), 1238 (1983)
Li, Z.-H.: Phys. Rev. D, Part. Fields 62(2), 024001 (2000)
Plebanski, J.F., Demianski, M.: Ann. Phys. 98(1), 98 (1976)
Regge, T., Wheeler, J.A.: Phys. Rev. 108(4), 1063 (1957)
Suzuki, H., Takasugi, E., Umetsu, H.: Prog. Theor. Phys. 100(3), 491 (1998)
Suzuki, H., Takasugi, E., Umetsu, H.: Prog. Theor. Phys. 102(2), 253 (1999)
Teukolsky, S.A.: Astrophys. J. 185, 635 (1973)
Torres del Castillo, G.F.: J. Math. Phys. 29(4), 971 (1988a)
Torres del Castillo, G.F.: J. Math. Phys. 29(9), 2078 (1988b)
Torres del Castillo, G.F.: J. Math. Phys. 30(2), 446 (1989)
Vishveshwara, C.V.: Phys. Rev. D, Part. Fields 1(10), 2870 (1970)
Zerilli, F.J.: Phys. Rev. D, Part. Fields 2(10), 2141 (1970)
Acknowledgements
This work was supported by NSFC Grant Nos. 11475148, 11075141, 11173021 and 11305140.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, M., Wang, X. & Li, Z. Spin field equations and Heun’s equations. Astrophys Space Sci 357, 139 (2015). https://doi.org/10.1007/s10509-015-2370-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-015-2370-z