We compute the quasinormal frequencies for scalar and electromagnetic perturbations of an improved Schwarzschild geometry in the framework of asymptotically safe gravity, which is one of the approaches to quantum gravity. Adopting the widely used WKB semi-classical approximation, we investigate the impact on the spectrum of the angular degree, the overtone number as well as the black hole mass. We summarize our numerical results in tables, and for better visualization, we show them graphically as well. All modes are found to be stable. Finally, we compare our numerical results with those corresponding to the classical Schwarzschild solution as well as to the results obtained using a different approach. Our findings show that i) a different cut-off identification does not affect the spectra significantly, and ii) for hypothetical objects with masses comparable to the Planck mass, the difference in the numerical values between the modes of the classical solution and the modes of the improved solution studied here is of the order of a few per cent. On the contrary, for realistic, astrophysical BHs no difference in the frequencies is observed.

我们在渐近安全引力的框架内计算改进的Schwarzschild几何体的标量和电磁扰动的准正规频率，这是实现量子引力的方法之一。采用广泛使用的WKB半经典近似，我们研究了角度度谱，泛音数以及黑洞质量对频谱的影响。我们将数值结果汇总在表格中，为了更好地可视化，我们还以图形方式显示了它们。发现所有模式都是稳定的。最后，我们将数值结果与对应于经典Schwarzschild解的数值结果以及使用不同方法获得的结果进行比较。我们的发现表明：i）不同的截止标识不会明显影响光谱，ii）对于质量与普朗克质量可比的假设物体，古典解的模态和改进的解的模态之间的数值差约为百分之几。相反，对于现实的天体BH，在频率上没有差异。