Universitetskaya nab. 7/9, Saint-Petersburg, 199034 Russia
Saint-Petersburg State University
Salatich A. A., Slavyanov S. Y.
Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
2019, Vol. 15, no. 1, pp. 79-85
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.