Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation

A.A. Salatich, S.Yu. Slavyanov
2019 Нелинейная динамика  
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
more » ... ion 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. As the most fascinating example the particular Teukolsky equation for the specific geometry of the boundary surface of the black hole is examined.
doi:10.20537/nd190108 fatcat:yydlpnbjufbmleblsrplq5dwta