Decay of massive scalar field in a Schwarzschild background

The decay of massive scalar field in the Schwarzschild black hole background is investigated here by consideration its quasinormal spectrum. It has been proved that the so-called quasi-resonant modes, which are arbitrary long living (purely real) modes, can exist only if the effective potential is not zero at least at one of the boundaries of the R-region. We have observed that the quasinormal spectrum exists for all field masses and proved both analytically and numerically that when n→∞ the real part of the frequencies approaches the same asymptotical value (ln3/(8πM)) as in the case of the massless field.