Long-lived quasinormal modes and oscillatory tails of the Bardeen spacetime

The Bardeen black hole stands as the first model of a regular black hole. Driven by the interpretations of Bardeen spacetime as a quantum-corrected Schwarzschild-like solution, we study quasinormal modes of a massive scalar field within this context. We have found that the damping rate of the massive scalar field decreases as the mass grows, leading to appearance of the arbitrarily long-lived modes. or quasiresonances. The massive term in the Bardeen case is also distinctive in two other respects. First, the overtones deviate from their massless limit at a much smaller rate than the fundamental mode, when the mass is turned on. This behavior overlaps with the so called outburst of overtones, which is deviation of overtones from their Schwarzschild values at an increasingly higher rate than happens for the fundamental mode. This high sensitivity of overtones occurs due to the quantum deformation near the event horizon. Finally, integration in the time domain shows that the oscillatory tails decay as $\ensuremath{\sim}{t}^{\ensuremath{-}( rac{8}{6}+\ensuremath{\ell})}$ at intermediate times and as $\ensuremath{\sim}{t}^{\ensuremath{-}1}$ at asymptotically late times, which is different from the Reissner-Nordstr\"om and Schwarzschild limits.