Antiquantization of the Double Confluent Heun equation. Teukolsky equation

A.A. Salatich, S. Y. Slavyanov

Research output

Abstract

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.
Original languageEnglish
Pages (from-to)79-85
JournalRussian Journal of Nonlinear Dynamics
Volume15
Issue number1
Publication statusPublished - 2019

Fingerprint

Geometry

Cite this

Salatich, A.A. ; Slavyanov , S. Y. / Antiquantization of the Double Confluent Heun equation. Teukolsky equation. In: Russian Journal of Nonlinear Dynamics. 2019 ; Vol. 15, No. 1. pp. 79-85.
@article{5187758030d6464d823156f727bf4c70,
title = "Antiquantization of the Double Confluent Heun equation. Teukolsky equation",
abstract = "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 Painlev{\'e} equation is derived by means of the antiquantization procedure. It turns out to be a particular case of P3. A general expression for any Painlev{\'e} 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.",
keywords = "Double confluent Heun equation, Painlev{\'e} equation P3, antiquantization, Teukolsky equation",
author = "A.A. Salatich and Slavyanov, {S. Y.}",
note = "A. A. Salatich, S. Yu. Slavyanov, “Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation”, Нелинейная динам., 15:1 (2019), 79–85",
year = "2019",
language = "English",
volume = "15",
pages = "79--85",
journal = "Nelineinaya Dinamika",
issn = "1816-448X",
publisher = "Institute of Computer Science",
number = "1",

}

Antiquantization of the Double Confluent Heun equation. Teukolsky equation. / Salatich, A.A.; Slavyanov , S. Y.

In: Russian Journal of Nonlinear Dynamics, Vol. 15, No. 1, 2019, p. 79-85.

Research output

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 - Nelineinaya Dinamika

JF - Nelineinaya Dinamika

SN - 1816-448X

IS - 1

ER -