Heun equation, Teukolsky equation, and type-D metrics

Abstract

Starting with the whole class of type-D vacuum backgrounds with cosmological constant we show that the separated Teukolsky equation for zero rest-mass fields with spin $s=\pm 2$ (gravitational waves), $s=\pm 1$ (electromagnetic waves) and $s=\pm 1/2$ (neutrinos) is an Heun equation in disguise.

27 pages, corrected typo in eq. (1)

References in corpus (3)

• Perturbations of Kerr-de Sitter Black Hole and Heun's Equations
• Massive Complex Scalar Field in a Kerr-Sen Black Hole Background: Exact Solution of Wave Equation and Hawking Radiation
• Massive complex scalar field in the Kerr-Sen geometry: Exact solution of wave equation and Hawking radiation

Cited by in corpus (29)

• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Heun Functions and Some of Their Applications in Physics
• Classes of Exact Solutions to the Teukolsky Master Equation
• Exact solutions of the Klein-Gordon equation in the Kerr-Newman background and Hawking radiation
• Teukolsky-Starobinsky Identities - a Novel Derivation and Generalizations
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
• Kerr-de Sitter Greybody Factors via Isomonodromy
• Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
• Potentials of the Heun class
• Heun-type solutions for Schwarzschild metric with electromagnetic fields
• Exact solution for wave scattering from black holes: Formulation
• Quantum Field Theory Applications of Heun Type Functions
• Exceptional point and hysteresis in perturbations of Kerr black holes
• Blandford-Znajek jets in MOdified Gravity
• Asymptotic behavior of Heun function and its integral formalism
• Exact wave-optical imaging of a Kerr-de Sitter black hole using Heun's equation
• Exact solution of the wave equation of a scalar particle in the zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times
• The hypergeneralized Heun equation in QFT in curved space-times
• Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution
• Special functions and reversible three-term recurrence formula (R3TRF)
• Electromagnetic analogue space-times, analytically and algebraically
• Complete polynomials using 3-term and reversible 3-term recurrence formulas (3TRF and R3TRF)
• A massless scalar particle coupled to the Wahlquist metric
• Semi-commuting and commuting operators for the Heun family
• Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field
• Charged massless scalar fields in a charged $C$-metric black hole: Exact solutions, Hawking radiation, and scattering of scalar waves
• Generalized Heun and Lamé's equations: factorization
• The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime
• On the Form of Solutions of Fuchsian differential Equations with n regular singular Points