Condition for the Superradiance Modes in Higher-Dimensional Rotating Black Holes with Multiple Angular Momentum Parameters

The condition for the existence of the superradiance modes is derived for the incident scalar, electromagnetic and gravitational waves when the spacetime background is a higher-dimensional rotating black hole with multiple angular momentum parameters. The final expression of the condition is 0 < ω < ∑ i miΩi, where Ωi is an angular frequency of the black hole and, ω and mi are the energy of the incident wave and the i-th azimuthal quantum number. The physical implication of this condition in the context of the brane-world scenarios is discussed. Email:[email protected] Email:[email protected] Email:[email protected] 1 Recently, much attention is paid to the various properties of the absorption and emission problems in the higher-dimensional black holes. This is mainly due to the fact that the braneworld scenarios [1–3] opens the possibility to make tiny black holes in the future colliders [4–7] by high-energy scattering. For the non-rotating black holes the complete absorption and emission spectra are calculated numerically in Ref. [8], where the effect of the number of extra dimensions n and the inner horizon radius r− on the spectra is carefully examined. It has been found in Ref. [8] that the presence of r− generally enhances the absorptivity and suppresses the emission rate while the presence of n reduces the absorptivity and increases the emission rate regardless of the brane-localized and bulk fields. In fact, this fact can be deduced by considering the Hawking temperature or by computing the effective potential generated by the horizon structure. Also, the ratio of the low-energy absorption cross section for the Dirac fermion to that for the scalar field is derived analytically [9] in the charged black hole background. For the case of the bulk fields this ratio factor becomes γ ≡ σ BL F σ S = 2 