×

zbMATH — the first resource for mathematics

Confluent Heun functions and the physics of black holes: resonant frequencies, Hawking radiation and scattering of scalar waves. (English) Zbl 1380.83167
Summary: We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr-Newman-Kasuya spacetime (dyon black hole) and a Reissner-Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein-Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied.

MSC:
83C57 Black holes
83C75 Space-time singularities, cosmic censorship, etc.
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abramov, D. I.; Kazakov, A. Y.; Ponomarev, L. I.; Slavyanov, S. Y.; Somov, L. N., J. Phys. B: At. Mol. Phys., 12, 1761, (1979)
[2] Bezerra, V. B.; Vieira, H. S.; Costa, A. A., Classical Quantum Gravity, 31, (2014)
[3] Chen, J.; Liao, H.; Wang, Y.; Chen, T., Eur. Phys. J. C, 73, 2395, (2013)
[4] Crispino, L. C.B.; Oliveira, E. S.; Higuchi, A.; Matsas, G. E.A., Phys. Rev. D, 75, (2007)
[5] Damour, T.; Deruelle, N.; Ruffini, R., Lett. Nuovo Cimento, 15, 257, (1976)
[6] Detweiler, S., Phys. Rev. D, 22, 2323, (1980)
[7] Dolan, S. R.; Dempsey, D., Classical Quantum Gravity, 32, (2015)
[8] Ernst, F. J., J. Math. Phys., 17, 54, (1976)
[9] Felice, F., Phys. Rev. D, 19, 451, (1979)
[10] Fiziev, P. P., Classical Quantum Gravity, 23, 2447, (2006)
[11] Fiziev, P. P., Classical Quantum Gravity, 27, (2010)
[12] Fiziev, P. P., J. Phys. A, 43, (2010)
[13] Fiziev, P.; Staicova, D., Phys. Rev. D, 84, (2011)
[14] Gaina, A. B.; Kochorbé, F. G., Zh. Eksp. Teor. Fiz., 92, 369, (1987)
[15] Glampedakis, K.; Andersson, N., Classical Quantum Gravity, 18, 1939, (2001)
[16] Handler, F. A.; Matzner, R. A., Phys. Rev. D, 22, 2331, (1980)
[17] Hawking, S. W., Comm. Math. Phys., 43, 199, (1975)
[18] M. Hortaçsu, 2015. arXiv:1101.0471v8 [math-ph].
[19] Kasuya, M., Phys. Rev. D, 25, 995, (1982)
[20] Kofinti, N. K., Internat. J. Theoret. Phys., 23, 991, (1984)
[21] Liao, H.; Chen, J.-H.; Liao, P.; Wang, Y.-J., Commun. Theor. Phys., 62, 227, (2014)
[22] Liao, H.; Chen, J.; Wang, Y., Internat. J. Modern Phys. D, 21, 1250045, (2012)
[23] Ronveaux, A., Heun’s differential equations, (1995), Oxford University Press New York · Zbl 0847.34006
[24] Rowan, D. J.; Stephenson, G., J. Phys. A: Math. Gen., 9, 1631, (1976)
[25] Sanchez, N. G., J. Math. Phys., 17, 688, (1976)
[26] Sánchez, N., Phys. Rev. D, 16, 937, (1977)
[27] Sánchez, N., Phys. Rev. D, 18, 1030, (1978)
[28] Simone, L. E.; Will, C. M., Classical Quantum Gravity, 9, 963, (1992)
[29] Slavyanov, S. Y.; Lay, W., Special functions, A unified theory based on singularities, (2000), Oxford University Press New York · Zbl 1064.33006
[30] Starobinsky, A. A., Zh. Eksp. Teor. Fiz., 64, 48, (1973)
[31] Vieira, H. S.; Bezerra, V. B.; Costa, A. A., Europhys. Lett., 109, 60006, (2015)
[32] Vieira, H. S.; Bezerra, V. B.; Muniz, C. R., Ann. Physics (NY), 350, 14, (2014)
[33] Vieira, H. S.; Bezerra, V. B.; Silva, G. V., Ann. Physics (NY), 362, 576, (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.