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 Nelin. Dinam., 2019, Volume 15, Number 1, Pages 79–85 (Mi nd642)

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

DOI: https://doi.org/10.20537/nd190108

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MSC: 34M55
Accepted:13.02.2019
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Citation: A. A. Salatich, S. Yu. Slavyanov, “Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation”, Nelin. Dinam., 15:1 (2019), 79–85

Citation in format AMSBIB
\Bibitem{SalSla19} \by A. A. Salatich, S. Yu. Slavyanov \paper Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation \jour Nelin. Dinam. \yr 2019 \vol 15 \issue 1 \pages 79--85 \mathnet{http://mi.mathnet.ru/nd642} \crossref{https://doi.org/10.20537/nd190108}