3D simulations of linearized scalar fields in Kerr spacetime

We investigate the behavior of a dynamical scalar field on a fixed Kerr background in Kerr-Schild coordinates using a (3+1)-dimensional spectral evolution code, and we measure the power-law tail decay that occurs at late times. We compare evolutions of initial data proportional to ${f\left(r\right)Y}_{\mathcal{l}m}(\theta ,\phi ),$ where $Y_{\mathcal{l}m}$ is a spherical harmonic and $(r,\theta ,\phi )$ are Kerr-Schild coordinates, to that of initial data proportional to ${f(r}_{\mathrm{BL}}{)Y}_{\mathcal{l}m}({\theta }_{\mathrm{BL}},\phi ),$ where ${(r}_{\mathrm{BL}},{\theta }_{\mathrm{BL}})$ are Boyer-Lindquist coordinates. We find that although these two cases are initially almost identical, the evolution can be quite different at intermediate times; however, at late times the power-law decay rates are equal.