Quasinormal modes of magnetized black hole

We investigate a charged, massive scalar field around a static, spherically symmetric black hole immersed into an external asymptotically uniform magnetic field B. It is shown that for given multipole number l there are 2l + 1 numbers of modes due to the Zeeman effect appearing by an interaction of the external magnetic and charged scalar fields introducing an effective mass of the scalar field mu(eff) = root mu(2) - mqB where m is the azimuthal number and q is the charge coupling constant. We calculate threshold value of effective mass in which quasinormal modes are arbitrarily long lived and beyond that value quasinormal modes vanish. In the case of mqB < 0 quasinormal modes are longer lived with larger oscillation frequencies. Whenever, magnetic and massive scalar fields satisfies condition mu(2)(eff) < 0, an instability appears, i.e., if qB > 0 or qB < 0 there is an instability for the values of azimuthal number m > mu(2)/qB or m < mu(2)/qB, respectively.