Decay of massive scalar field in a black hole background immersed in magnetic field

We evaluate quasinormal modes of a massive scalar field of the Ernst spacetime, an exact solution of the Einstein–Maxwell equations, describing a black hole immersed in a uniform magnetic field B. It is well known that the quasinormal spectrum for a massive scalar field in the vicinity of the magnetized black holes acquires an effective mass $$\mu _\mathrm{eff}= \sqrt{4B^2 m^2+\mu ^2}$$ , where m is the azimuthal number and $$\mu $$ is the mass of scalar field. The numerical result shows that increasing of the field effective mass and the magnetic field B gives rise to decreasing of the imaginary part of the quasinormal modes until reaching a vanishing damping rate.

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