Аннотация
It is known that the imaginary parts of the quasi normal mode (QNM)
frequencies for the Schwarzschild black hole are evenly spaced with a spacing
that depends only on the surface gravity. On the other hand, for massless
minimally coupled scalar fields, there exist no QNMs in the pure DeSitter
spacetime. It is not clear what the structure of the QNMs would be for the
Schwarzschild-DeSitter (SDS) spacetime, which is characterized by two different
surface gravities. We provide a simple derivation of the imaginary parts of the
QNM frequencies for the SDS spacetime by calculating the scattering amplitude
in the first Born approximation and determining its poles. We find that, for
the usual set of boundary conditions in which the incident wave is scattered
off the black hole horizon, the imaginary parts of the QNM frequencies have a
equally spaced structure with the level spacing depending on the surface
gravity of the black hole. Several conceptual issues related to the QNM are
discussed in the light of this result and comparison with previous work is
presented.
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