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It is known that the imaginary parts of the quasi normal mode (QNM)frequencies for the Schwarzschild black hole are evenly spaced with a spacingthat depends only on the surface gravity. On the other hand, for masslessminimally coupled scalar fields, there exist no QNMs in the pure DeSitterspacetime. It is not clear what the structure of the QNMs would be for theSchwarzschild-DeSitter (SDS) spacetime, which is characterized by two differentsurface gravities. We provide a simple derivation of the imaginary parts of theQNM frequencies for the SDS spacetime by calculating the scattering amplitudein the first Born approximation and determining its poles. We find that, forthe usual set of boundary conditions in which the incident wave is scatteredoff the black hole horizon, the imaginary parts of the QNM frequencies have aequally spaced structure with the level spacing depending on the surfacegravity of the black hole. Several conceptual issues related to the QNM arediscussed in the light of this result and comparison with previous work ispresented.Comment: Revised version. Accepted in Phys. Rev.

Quasinormal modes in Schwarzschild–de Sitter spacetime: A simple derivation of the level spacing of the frequencies