Solutions to a generalized spheroidal wave equation in molecular physics and general relativity, and an analysis of the quasi-normal modes of Kerr black holes

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1985

OSTI ID:5765751

Leaver, E W

The purpose of this dissertation is to present important new analytic representations for solutions to the generalized spheroidal wave equation x(x-x/sub 0/)d/sup 2/y/dx/sup 2/ + (B/sub 1/ + B/sub 2/x)dy/dx + (omega/sup 2/x(x-x/sub 0/) - 2(eta)(omega)(x - x/sub 0/) + B/sub 3/)y = 0. Discussion of solutions on the angular interval (0 less than or equal to x less than or equal to x/sub 0/) is included, but the major emphasis is on the radial functions for which (x/sub 0/ less than or equal to x < infinity). The study starts with the 1930s work of E. Hylleraas, G. Jaffe, W.G. Baber, and H.R. Hasse, and P.M. Morse. Rigorous proof is given for the convergence of Morse's spherical Bessel function expansion for ordinary spheroidal wavefunctions. The Jaffe-Baber-Hasse eigenfunction representation is shown to yield computationally elegant eigensolutions to Teukolsky's equations, and extensive discussion is given to the quasi-normal mode problem and the behavior of the quasi-normal frequencies as function of I-pole moment and black hole angular momentum. An integral relating radial functions is derived that connects the Jaff-Baber-Hasse modified power series representation to the Laguerre polynomial expansion of Hylleraas, and which gives an integral equation for scalar field quasi-normal models. Two confluent hypergeometric function expansions are discussed, and a powerful new representation is given expressing the generalized spheroidal wavefunctions as series of Coulomb wavefunctions.

• Research Organization: Utah Univ., Salt Lake City (USA)
• OSTI ID: 5765751
• Country of Publication: United States
• Language: English

Related Subjects

640102* -- Astrophysics &amp; Cosmology-- Stars &amp; Quasi-Stellar
Radio &amp; X-Ray Sources
657003 -- Theoretical &amp; Mathematical Physics-- Relativity &amp; Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
BLACK HOLES
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
KERR FIELD
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
WAVE FUNCTIONS