The preparation of a-Si: H films by DIBS deposition method with lower energy side ions.

Suzuki, Yoshihiko; Ogawa, Soichi; Takiguchi, Katsuki; Yotsuya, Tsutomu; Nagakubo, M.

doi:10.3131/jvsj.28.354

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“…Although the use of our solution in this paper is less clear than that for the Kerr geometry case, we believe that our solution will be relevant to the physical world, especially in the early stage of the universe where the cosmological constant plays important role. By using our solution, we can derive the analytic expression of the decay rate for emission of massless particles from the Kerr-de Sitter or the Kerr-Newman-de Sitter black hole [11], which can be used to examine a correspondence between quantum gravity on anti-de Sitter space and a conformal field theory defined on its boundary [12,13], Now we observe that the transcendental equation which determine ν given in Eq. (3.6) contains coefficients as β ν n (s) and a special combination α ν n−1 (s)γ ν n (s).…”

Section: Summary and Discussionmentioning

confidence: 99%

Analytic Solutions of the Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

Suzuki

Takasugi

Umetsu

1999

Progress of Theoretical Physics

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An analytic solution of the Teukolsky equation in Kerr-de Sitter and Kerr-Newman-de Sitter geometries is presented, and the properties of this solution are examined. In particular, we show that our solution satisfies the Teukolsky-Starobinsky identities explicitly and fix the relative normalization between solutions with spin weights s and −s. §1. IntroductionIn a series of papers, Mano, Suzuki and Takasugi 1), 2) have constructed an analytic solution of the perturbation equation of massless fields in Kerr geometries which is commonly called the Teukolsky equation. 3) This solution enabled us to investigate various properties of black holes analytically, 4) the scattering problem of a particle emitted in a black hole, an analytical expression for the absorption rate by a Kerr black hole, which was one of the main interests of Chandrasekhar, 5) and the Teukolsky-Starobinsky identities.Our solution is expressed in the form of a series of hypergeometric functions and Coulomb wave functions. The coefficients of this series are determined by solving three-term recurrence relations. Two series have different convergence regions, and they are matched in the region where both series converge. This method turns out to be quite powerful in practical calculations and is successfully applied to examine gravitational waves from a binary in a post-Newtonian expansion; to construct the template of the gravitational wave emitted from a particle moving around a Kerr black hole 6) and the rate of absorption of a gravitational wave by the black hole. 7)In a previous paper, 8) Suzuki, Takasugi and Umetsu extended this method to solve the perturbation equations of massless fields (the Teukolsky equation) in Kerrde Sitter and Kerr-Newman-de Sitter geometries. We found transformations such that both the angular and the radial equations are reduced to Heun's equation. 9) The solution of Heun's equation is expressed in the form of a series of hypergeometric functions, and its coefficients are determined by three-term recurrence relations, similarly to the Kerr geometry case. It should be noted that electromagnetic fields and gravitational fields couple to each other in Kerr-Newman-de Sitter geometries and do not obey the equation we considered there, although the fields obey the * )

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Section: Summary and Discussionmentioning

confidence: 99%