AI 中文总结
该研究检验了高维Reissner-Nordström黑洞引力微扰中准正则模与灰体因子的对应关系，发现该对应在多数微扰类型下有效，且适用范围比WKB假设更广。
AI 中文摘要
我们研究了高维Reissner-Nordström黑洞的准正则模（QNMs）与灰体因子（GBFs）之间的对应关系。考虑这些黑洞的引力微扰，我们系统地计算了标量、矢量和张量微扰的QNMs和GBFs，包括标量和矢量微扰的$(+)$和$(-)$类型，以检验该对应关系的有效性。QNMs采用连分式方法计算，当每种微扰类型和黑洞参数组的Frobenius级数奇点结构需要时，应用中点积分法。我们通过将对应关系得到的GBFs与数值积分得到的GBFs进行比较，评估了每个时空维度$D$和黑洞电荷下对应关系的准确性。对应关系对标量$(+)$、矢量$(+)$、矢量$(-)$和张量微扰的GBFs提供了良好的近似。然而，对于标量$(-)$类型，在$D > 6$的低到中等电荷下，对应关系表现出显著偏差。在较高电荷下，尽管有效势呈现双峰结构，与对应关系基于Wentzel-Kramers-Brillouin（WKB）推导的假设不一致，但对应关系仍恢复了合理的准确性。与其他类型随$D$增大对应关系变差的情况相反，标量$(-)$类型在$D=8$时比$D=7$时更准确。此外，对于近极端黑洞的矢量$(-)$微扰，即使在$D>6$时势出现双峰结构，对应关系也表现良好。这些结果表明，该对应关系的适用范围比WKB近似假设所预期的更广。
英文摘要
We investigate the correspondence between quasinormal modes (QNMs) and grey-body factors (GBFs) of higher-dimensional Reissner-Nordström black holes. Considering gravitational perturbations of these black holes, we systematically compute the QNMs and GBFs for scalar, vector, and tensor perturbations, including the $(+)$ and $(-)$ types of scalar and vector perturbations, to examine the validity of the correspondence. The QNMs are computed using the continued fraction method, and the integration-through-midpoints method is applied when required by the singularity structure of the Frobenius series for each perturbation type and set of black-hole parameters. We evaluate the accuracy of the correspondence for each spacetime dimension $D$ and black-hole charge by comparing the GBFs obtained from the correspondence with those obtained by numerical integration. The correspondence provides a good approximation to the GBFs for the scalar($+$), vector($+$), vector($-$), and tensor perturbations. However, for the scalar($-$) type, the correspondence exhibits pronounced deviations at low to intermediate charges in $D > 6$. At higher charges, it recovers reasonable accuracy despite the effective potential exhibiting a double-peak structure inconsistent with the assumptions underlying the Wentzel-Kramers-Brillouin (WKB)-based derivation of the correspondence. In contrast to the other types, for which the correspondence deteriorates as $D$ increases, the scalar($-$) type is more accurate in $D=8$ than in $D=7$. Furthermore, the correspondence performs well for the vector($-$) perturbation of near-extreme black holes, even though the potential develops a double-peak structure in $D>6$. These results indicate that the correspondence is applicable over a broader range than expected from the assumptions of the WKB approximation.
Comments48 pages, 54 figures
