Quasinormal modes of magnetized black hole

Abstract

We investigate charged, massive scalar field around static, spherically symmetric black hole immersed into an external asymptotically uniform magnetic field $B$. It is shown that for given multipole number $\ell$ there are $2\ell +1$ 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 ${\mu }_{\mathrm{eff}}=\sqrt{{\mu }^2-mqB}$ 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 ${\mu }_{\mathrm{eff}}^2<0$, 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.

8 pages, 2 tables, 4 figures. Accepted for publication in Phys. Rev. D

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