Telling late-time tails for a massive scalar field in the background of brane-localized black holes

We examine perturbations of a massive scalar field around spherically symmetric, brane-localized black holes. Although the ringdown and asymptotic tails of various brane-world black holes have been extensively studied, there has been no analysis of the massive late-time tails for the simplest Schwarzschild-like, brane-localized black hole to date. We demonstrate that after the ringdown phase, two stages of oscillatory tails emerge - intermediate and asymptotic. The asymptotic decay law is distinct from those associated with Schwarzschild or Reissner-Nordstrom solutions.