Correspondence between Quasinormal Modes and Grey-Body Factors of Schwarzschild-Tangherlini Black Holes

초록

We investigate the correspondence between the quasinormal modes and grey-body factors of Schwarzschild-Tangherlini black holes. Gravitational perturbations in higher-dimensional black holes can be classified into scalar, vector, and tensor types. Considering the dimension-dependent forms of their effective potentials, the correspondence is examined for each dimension and perturbation mode. Accurate quasinormal modes are computed by suitably adopting the continued fraction and integration-through-midpoints methods, depending on the structure of the singularity. The grey-body factor can be obtained analytically through its correspondence with the quasinormal mode, and its accuracy is analyzed by calculating its difference from the numerically computed grey-body factor. The correspondence fails for $l=2$ scalar gravitational perturbations in $D\ge 7$ because the form of the potential is markedly different from that in four dimensions. The vector and tensor perturbation types exhibit good correspondence accuracy in all cases. The breakdown of the correspondence is rigorously shown to stem from multiple potential barriers, and its applicability to each mode in higher dimensions is assessed.

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