TY - JOUR

T1 - Antiquantization of the Double Confluent Heun equation. Teukolsky equation

AU - Salatich, A.A.

AU - Slavyanov , S. Y.

N1 - A. A. Salatich, S. Yu. Slavyanov, “Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation”, Нелинейная динам., 15:1 (2019), 79–85

PY - 2019

Y1 - 2019

N2 - 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 P3. 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.

AB - 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 P3. 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.

KW - Double confluent Heun equation

KW - Painlevé equation P3

KW - antiquantization

KW - Teukolsky equation

UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=nd&paperid=642&option_lang=rus

M3 - Article

VL - 15

SP - 79

EP - 85

JO - Russian Journal of Nonlinear Dynamics

JF - Russian Journal of Nonlinear Dynamics

SN - 2658-5324

IS - 1

ER -