Source-Driven Tails in Kerr Spacetime: Nonlinear effects in Late-Time Behavior

We present the long-duration time-domain simulations of scalar-field tails in Kerr spacetimes driven by \emph{outgoing} multipolar sources. Extending the recent work in the literature from Schwarzschild to rotating black holes, we evolve sources with ${\mathrm{\ell }}^{\mathrm{\prime }}=\{0,1,2,3,4\}$ on backgrounds with dimensionless spin $a\mathrm{/}M=\{0.0,0.8,1.0\}$ and extract the late-time decay rates of measured modes $\mathrm{\ell }\le 4$ for a nonlinearity-inspired outgoing source with a $1\mathrm{/}{r}^2$ fall-off. In all cases we find the inverse power-law index $p_{\mathrm{\ell }{\mathrm{\ell }}^{\mathrm{\prime }}}$ to be larger than the source-free Price law values by one unit, i.e. $p_{\mathrm{\ell }{\mathrm{\ell }}^{\mathrm{\prime }}}^{\text{sourced}}=p_{\mathrm{\ell }{\mathrm{\ell }}^{\mathrm{\prime }}}^{\text{Price}}+1$. We also include a power-law index value computation for a similar source-driven gravitational wave case $(\mathrm{\ell },m)=(4,4)$ and confirm closely related results in the recent literature.