1
$\begingroup$

I have been trying to derive the Teukolsky equation via the Newman-Penrose formalism. I have derived the following formula (see Eq. (2.14) in Teukolsky's paper)

\begin{equation} (*) \left[(\Delta +3\gamma - \gamma^*+4\mu + \mu^*)(D+4\epsilon-\rho)-(\delta^*-\tau^*+\beta^*+3\alpha+4\pi)(\delta-\tau+4\beta)-3\psi_2\right]\psi_4 = 0. \end{equation}

The Greek letters (except for $\psi_4$) are all defined with respect to the Kerr background.

What I am struggling with is: deriving the actual wave equation (Eq. (4.7) in Teukolsky's paper) for $\psi_4$ using the Kinnersly tetrad (see Eq (4.4)-(4.6) in Teukolsky's paper) in Boyer-Lindquist coordinates, starting from Eq.(*). I am plugging in the defined values like $\Delta=l^{\mu}\partial_{\mu}$, etc. but I cannot recover Teukolsky's full equation: I have the wrong coefficients for the $\partial_{\theta}\psi_4$, $\partial_{\phi}\psi_4$, $\partial_r\psi_4$, and $\psi_4$ components.

I would greatly appreciate notes on deriving the Teukolsky equation, a link to a mathematica notebook, or a demonstration in someones answer on going from the Newman-Penrose Eq.(*) to the Teukolsky equation in Boyer-Lindquist coordinates.

$\endgroup$
0
$\begingroup$

I figured out what my problem was: If one looks at Table 1 of Teukolsky's paper, in fact I should be setting \begin{equation} \psi_4= \rho^4\psi, \end{equation} and then one recovers the Teukoslky equation for a spin $-2$ field.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.