Geodesic
Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 1, pp. 79-85

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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: Teukolsky equation.
Mots-clés : Double confluent Heun equation, antiquantization, Painlevé equation $P^3$ 
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A. A. Salatich; S. Yu. Slavyanov. Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 1, pp. 79-85. http://geodesic.mathdoc.fr/item/ND_2019_15_1_a7/