We compute the quasinormal spectra for scalar, Dirac and electromagnetic perturbations of the Schwarzschild–de Sitter geometry in the framework of scale-dependent gravity, which is one of the current 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 scale-dependent parameter for fixed black hole mass and cosmological constant. We summarize our numerical results in tables, and for better visualization, we show them graphically as well. All modes are found to be stable. Our findings show that both the real part and the absolute value of the imaginary part of the frequencies increase with the parameter $ϵ$ that measures the deviation from the classical geometry. Therefore, in the framework of scale-dependent gravity the modes oscillate and decay faster in comparison with their classical counterparts.

我们在与比例有关的引力框架内计算Schwarzschild-de Sitter几何的标量，狄拉克和电磁扰动的准正态谱，这是当前量子引力的一种方法。采用广泛使用的WKB半经典近似，我们研究了固定黑洞质量和宇宙常数对角度谱，泛音数以及与尺度有关的参数的影响。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。我们的发现表明，频率的实部和虚部的绝对值均随参数的增加而增加。$ϵ$测量与经典几何的偏差。因此，在与比例有关的重力框架下，与经典模式相比，模式振荡和衰减更快。