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Example: spheroid program

This is a second implementation of the function sw_spheroid() which is used to compute the spin-weighted spheroidal wave function associated with a quasinormal ringdown mode of a Kerr black hole with a certain (specified in the code) dimensionless angular momentum parameter. To invoke the program, type:

spheroid $s$ $\ell$ $m$
for the desired (integer) values of $s$, $\ell$, and $m$ ($\ell\ge\vert s\vert$ and $\vert m\vert\le\ell$) of the desired mode. The output is three columns of data: the first column is the independent variable $\mu$ between $-1$ and $+1$, the second column is the value of the real part of  ${}_sS_{\ell m}(\mu)$, and the third column is the value of the imaginary part of  ${}_sS_{\ell m}(\mu)$. Figure [*] depicts the output for the spin-weighted spheroidal wave function  ${}_{-2}S_{22}(\mu)$.

Figure: A plot of the real and imaginary parts of the $\ell=m=-s=2$ spin-weighted spheroidal wave function, ${}_{-2}S_{22}(\mu)$, associated with a black hole with dimensionless angular momentum parameter $\hat{a}=0.98$. The imaginary part is scaled by a factor of ten.
\begin{figure}\begin{center}
\index{colorpage}
\epsfig{file=Figures/spheroid.eps,height=7.5cm}\end{center}\end{figure}

Includes/spheroid.tex

Author: Jolien Creighton, jolien@tapir.caltech.edu


next up previous contents
Next: Function: qn_ring() Up: GRASP Routines: Black hole Previous: Example: spherical program   Contents
Bruce Allen 2000-11-19