7 research outputs found
High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation
We fully determine a uniformly valid asymptotic behaviour for large and fixed of the angular solutions and eigenvalues of the
spin-weighted spheroidal differential equation. We fully complement the
analytic work with a numerical study.Comment: The .tar.gz file should contain 1 tex file, 24 figures in .ps format
and 1 bibliography file in .bbl format. All these files are located in the
same director
Asymptotic Spectroscopy of Rotating Black Holes
We calculate analytically the transmission and reflection amplitudes for
waves incident on a rotating black hole in d=4, analytically continued to
asymptotically large, nearly imaginary frequency. These amplitudes determine
the asymptotic resonant frequencies of the black hole, including quasinormal
modes, total-transmission modes and total-reflection modes. We identify these
modes with semiclassical bound states of a one-dimensional Schrodinger
equation, localized along contours in the complexified r-plane which connect
turning points of corresponding null geodesics. Each family of modes has a
characteristic temperature and chemical potential. The relations between them
provide hints about the microscopic description of the black hole in this
asymptotic regime.Comment: References adde