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This article is cited in 3 scientific papers (total in 3 papers)
Mathematical problems of nonlinearity
Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
A. A. Salatich, S. Yu. Slavyanov Saint-Petersburg State University, Universitetskaya nab. 7/9, Saint-Petersburg, 199034 Russia
Abstract:
Different forms of the double confluent Heun equation are studied. A generalized Riemann scheme for these forms is given. An equivalent first-order system is introduced. This system can be regarded from the viewpoint of the monodromy property. A corresponding Painlevé equation is derived by means of the antiquantization procedure. It turns out to be a particular case of $P^3$. A general expression for any Painlevé equation is predicted. A particular case of the Teukolsky equation in the theory of black holes is examined. This case is related to the boundary between spherical and thyroidal geometries of a black hole. Difficulties for its antiquantization are shown.
Keywords:
Double confluent Heun equation, antiquantization, Painlevé equation $P^3$, Teukolsky equation.
Received: 16.12.2018 Accepted: 13.02.2019
Citation:
A. A. Salatich, S. Yu. Slavyanov, “Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation”, Rus. J. Nonlin. Dyn., 15:1 (2019), 79–85
Linking options:
https://www.mathnet.ru/eng/nd642 https://www.mathnet.ru/eng/nd/v15/i1/p79
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Abstract page: | 223 | Full-text PDF : | 89 | References: | 37 |
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