The hypergeneralized Heun equation in quantum field theory in curved space-times

Batic, Davide; Sandoval, Manuel

doi:10.2478/s11534-009-0107-8

Cited by 8 publications

(14 citation statements)

References 13 publications

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“…Unfortunately this is again less useful than one might suppose, this time because relatively little is known about the analytical behaviour of Heun functions -this is an area of ongoing research in mathematical analysis [8].…”

Section: Regge-wheeler Equationmentioning

confidence: 99%

Bounding the greybody factors for Schwarzschild black holes

2008

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Greybody factors in black hole physics modify the naive Planckian spectrum that is predicted for Hawking radiation when working in the limit of geometrical optics. We consider the Schwarzschild geometry in (3+1) dimensions, and analyze the Regge-Wheeler equation for arbitrary particle spin s and wave-mode angular momentum ℓ, deriving rigourous bounds on the greybody factors as a function of s, ℓ, wave frequency ω, and the black hole mass m.

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Section: Regge-wheeler Equationmentioning

confidence: 99%

Bounding the greybody factors for Schwarzschild black holes

2008

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“…Note that when a = Λ = 0 the angular eigenfunctions S ± reduce to the well-known spin-weighted spherical harmonics whereas for a = 0 = Λ the same eigenfunctions satisfy a Heun equation [31]. Finally, in the general case of non vanishing values of the parameters Λ and a it has been shown in [32] that S ± obey a generalized Heun equation (GHE). Since the GHE has been scarcely studied in the mathematical literature made exceptions of [33] and [34], the next section will be devoted to study the spectrum of the angular eigenvalue problem, the dependence of the eigenvalues upon the relevant physical parameters, and to obtain series representations for the eigenfunctions.…”

Section: The Dirac Equation In the Kerr-de Sitter Metricmentioning

confidence: 99%

The Dirac Equation in the Kerr-de Sitter Metric

et al. 2018

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We consider a Fermion in the presence of a rotating black hole immersed in a universe with positive cosmological constant. After deriving new formulae for the event, Cauchy and cosmological horizons we adopt the Carter tetrad to separate the aforementioned equation into a radial and angular equation. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that can be interpreted as the square root of the squared total angular momentum operator. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.

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“…Our approach is in accord with the Chandrasekhar expectation that the Newman-Penrose formalism for perturbations of the Kerr metric may "...enable us to discover new classes of identities among the special functions of mathematical physics when they occur as solutions of Einstein's equations" and his suggestion to "...include Teukolsky's functions among "special" functions of mathematical physics..." [3]. Today it is clear that for realization of this general idea we need to use the Heun functions and some of their generalizations [17].…”

Section: Introductionmentioning

confidence: 99%

Teukolsky-Starobinsky identities: A novel derivation and generalizations

Fiziev

2009

Phys. Rev. D

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We present a novel derivation of the Teukolsky-Starobinsky identities, based on properties of the confluent Heun functions. These functions define analytically all exact solutions to the Teukolsky master equation, as well as to the Regge-Wheeler and Zerilli ones. The class of solutions, subject to Teukolsky-Starobinsky type of identities is studied. Our generalization of the Teukolsky-Starobinsky identities is valid for the already studied linear perturbations to the Kerr and Schwarzschild metrics, as well as for large new classes of of such perturbations which are explicitly described in the present article. Symmetry of parameters of confluent Heun's functions is shown to stay behind the behavior of the known solutions under the change of the sign of their spin weights. A new efficient recurrent method for calculation of Starobinsky's constant is described.

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The hypergeneralized Heun equation in quantum field theory in curved space-times

Abstract: Abstract:We show for the first time the role played by the hypergeneralized Heun equation (

Cited by 8 publications

References 13 publications

Bounding the greybody factors for Schwarzschild black holes

Bounding the greybody factors for Schwarzschild black holes

The Dirac Equation in the Kerr-de Sitter Metric

Teukolsky-Starobinsky identities: A novel derivation and generalizations

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