Mathematical problems of nonlinearity
Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
A. A. Salatich, S. Yu. Slavyanov
Saint-Petersburg State University, Universitetskaya nab. 7/9, Saint-Petersburg, 199034 Russia
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.
Double confluent Heun equation, antiquantization, Painlevé equation $P^3$, Teukolsky equation
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A. A. Salatich, S. Yu. Slavyanov, “Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation”, Nelin. Dinam., 15:1 (2019), 79–85
Citation in format AMSBIB
\by A. A. Salatich, S. Yu. Slavyanov
\paper Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
\jour Nelin. Dinam.
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