It was first pointed out by Koyama and Tomimatsu that, under reasonable
assumptions, the asymptotic late-time tails of massive scalar perturbations in
the far zone of spherically symmetric black hole spacetimes decays universally
as $t^{-5/6}$. The late-time tail is furnished by the contribution from the
branch cut of the frequency-domain Green’s function, which is constructed in
terms of two appropriate solutions of the corresponding homogeneous equation.
The present study is focused on some particular forms of the in-going wave that
were not explicitly considered in the original derivations but nonetheless have
been taken into account in the literature by other authors. In this regard, we
reassess the authors’ arguments and provide a detailed complimentary analysis
that covers a few specific aspects. For some particular cases, the tail is
found to possess the form $t^{-1}$. We also discuss the possible implications
of the present findings.

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