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

We investigate the correspondence between quasinormal modes and grey-body factors for the five-dimensional Schwarzschild--Tangherlini black hole. The quasinormal modes of gravitational perturbations are computed numerically using the continued fraction method. Particularly, we analyze the scalar, vector, and tensor types of perturbations, noting that the tensor type only exists in spacetimes with more than four dimensions. The grey-body factors are then calculated analytically via the correspondence, using data from the fundamental quasinormal mode and the first overtone. We then compute the grey-body factors independently using a numerical method and find that the results from the two methods coincide. This demonstrates 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.