Aleksandr Salatich
Universitetskaya nab. 7/9, SaintPetersburg, 199034 Russia
SaintPetersburg State University
Publications:
Salatich A. A., Slavyanov S. Y.
Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
2019, Vol. 15, no. 1, pp. 7985
Abstract
Different forms of the double confluent Heun equation are studied. A generalized Riemann
scheme for these forms is given. An equivalent firstorder 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.
