Teukolsky point-particle mode module#
The TeukolskyMode class constructs modes of the so-called extended homogeneous solutions to the radial Teukolsky equation for a point-particle source on a bound periodic geodesic,
\[\begin{split}\begin{align}
\Psi_s &= \Psi_s^+ \Theta(r-r_p) + \Psi_s^- \Theta(r_p-r),
\\
\Psi_s^\pm &= \sum_{jmkn}Z^{\mathrm{Up/In}}_{sjmkn}R^{\mathrm{Up/In}}_{sjmkn}(r)S_{sj\gamma_{mkn}}(\theta)e^{im\phi}e^{-i\omega_{mkn}t},
\end{align}\end{split}\]
where we have the mode frequencies \(\omega_{mkn} = m\Omega_\phi + k \Omega_\theta + n \Omega_r\), the discrete spheroidicity \(\gamma_{mkn} = a\omega_{mkn}\).