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.
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License
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.
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