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# Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation

2019, Vol. 15, no. 1, pp.  79-85

Author(s): Salatich A. A., Slavyanov S. Y.

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
Citation: Salatich A. A., Slavyanov S. Y., Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 1, pp.  79-85
DOI:10.20537/nd190108