Mode coupling mechanism for late-time Kerr tails

Understand

We consider the decay rate for scalar fields in Kerr spacetime.

• We consider pure initial (azimuthal) multipoles $\ell'$ with respect to the class which includes Boyer-Lindquist coordinates, and focus attention on the decay rate of the multipole $\ell$.
• We use an iterative method proposed by Gleiser, Price, and Pullin, and identify the mode coupling mechanism through the iterations in powers of the square of the Kerr black hole's specific angular momentum that gives rise to a decay rate formula recently proposed by Zengino\u{g}lu, Khanna, and Burko.
• Modes $\ell$ may be excited through different channels, each leading to its own decay rate.