Correspondence between quasinormal modes and greybody factors in five-dimensional black holes

초록

We have investigated the correspondence between quasinormal modes and greybody factors for the fivedimensional Schwarzschild-Tangherlini black hole. The quasinormal modes of gravitational perturbations are computed numerically using the continued fraction method. Particularly, we have analyzed the scalar, vector, and tensor types of perturbations, revealing that the tensor type only exists in spacetimes with more than four dimensions. Then, the greybody factors are calculated analytically via the correspondence using data from the fundamental quasinormal mode and the first overtone. Next, the greybody factors are computed independently using a numerical method. Notably, the results obtained from the two methods coincide, demonstrating that the correspondence holds with high accuracy for all three types of gravitational perturbations. Furthermore, our results extend the validity of the correspondence to the tensor type, which can only be tested in spacetimes with more than four dimensions.

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