Late-time Kerr tails: generic and non-generic initial data sets, "up" modes, and superposition

Abstract

Three interrelated questions concerning Kerr spacetime late-time scalar-field tails are considered numerically, specifically the evolutions of generic and non-generic initial data sets, the excitation of "up" modes, and the resolution of an apparent paradox related to the superposition principle. We propose to generalize the Barack-Ori formula for the decay rate of any tail multipole given a generic initial data set, to the contribution of any initial multipole mode. Our proposal leads to a much simpler expression for the late-time power law index. Specifically, we propose that the late-time decay rate of the $Y_{\ell m}$ spherical harmonic multipole moment because of an initial $Y_{{\ell }^{\prime }m}$ multipole is independent of the azimuthal number $m$, and is given by $t^{-n}$, where $n={\ell }^{\prime }+\ell +1$ for $\ell <{\ell }^{\prime }$ and $n={\ell }^{\prime }+\ell +3$ for $\ell \ge {\ell }^{\prime }$. We also show explicitly that the angular symmetry group of a multipole does not determine its late-time decay rate.

12 pages, 13 figures, 4 tables. Substantially revised manuscript

References in corpus (2)

• High accuracy simulations of Kerr tails: coordinate dependence and higher multipoles
• Late-time Kerr tails revisited

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