= Scalar wave separation in Kerr spacetime
{title2=$\Psi=e^{-i\omega t+i m\phi}R(r)\Theta(\theta)$}
For the massless <Klein-Gordon equation> on a <Kerr black hole>, the <covariant wave operator> separates into radial and angular <ordinary differential equations>. With $K=(r^2+a^2)\omega-am$ and angular <separation constant> $\Lambda$, the radial equation is $(\Delta R')'+[K^2/\Delta-a^2\omega^2+2am\omega-\Lambda]R=0$. The angular equation is $(\sin\theta\,\Theta')'/\sin\theta+[a^2\omega^2\cos^2\theta-m^2/\sin^2\theta+\Lambda]\Theta=0$. No extra radial factor is included in the displayed ansatz.
Back to article page
