Power law tails induced by nonlinearities of general relativity (“sourced” or “nonlinear” tails) were recently shown to dominate the late time waveform of Schwarzschild black hole ringdowns. We extend the analytical results regarding such nonlinear tails from Schwarzschild to Kerr black holes by studying the Teukolsky equation. Using a far field approximation to the radial Green’s function, we analytically derived the tail power law for spin-weight $s\ne 0$, harmonic mode ($\ell m$) and source decay $r^{-\beta }$. Specifically, we found a $t^{-\ell -\beta -s}$ tail for $\beta \le 1$ or $\beta \ge \ell -s+2$, and a $t^{-2\ell -3}$ Price tail for $2\le \beta \le \ell -s+1$. Our numerical tests were in exact agreement with these analytic results. We also demonstrate the dynamical formation of such nonlinear tails for a massless scalar by numerically solving the Teukolsky equation. In all numerical results, Kerr black hole nonlinear tails have the same power laws as that for Schwarzschild black holes, as expected from the Minkowski nature of the spacetime in the far field region.

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• Classical black holes
• General relativity
• Gravitation
• Gravitational waves
• Numerical simulations in gravitation & astrophysics