We calculate gravitational perturbation quasinormal modes (QNMs) of non-singular Bardeen black holes (BHs) and singularity-free BHs in conformal gravity and examine their spectra in wave dynamics comparing with standard BHs in general relativity. After testing the validity of the approximate signal-to-noise ratio (SNR) calculation for different space based interferometers, we discuss the SNR of non-singular BHs in single-mode gravitational waveform detections in LISA, TianQin and TaiJi. We explore the impact of the Bardeen parameter and the conformal factor on the behavior of the SNR and find that in comparison with the standard Schwarzschild BHs, the increase of non-singular parameters leads to higher SNR for more massive non-singular BHs. We also examine the effect of the galactic confusion noise on the SNR and find that a dip appears in SNR due to such noise. For non-singular BHs, with the increase of the non-singular parameters the dip emerges for more massive BHs. Imprints of non-singular BHs on peaks and dips in SNR imply that non-singular BHs are likely to be distinguished from the standard Schwarzschild BHs when BHs are sufficient massive. The detections of non-singular BHs are expected to be realized more likely by LISA or TaiJi.

中文翻译：

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在引力扰动中探索非奇异黑洞

我们计算了共形引力中非奇异巴丁黑洞 (BHs) 和无奇点 BHs 的引力扰动准正规模式 (QNMs)，并与广义相对论中的标准 BHs 比较了它们在波动力学中的光谱。在测试了不同天基干涉仪的近似信噪比 (SNR) 计算的有效性后，我们讨论了 LISA、天琴和太极单模引力波形检测中非奇异 BH 的 SNR。我们探索了 Bardeen 参数和共形因子对 SNR 行为的影响，发现与标准 Schwarzschild BH 相比，非奇异参数的增加导致更大质量非奇异 BH 的更高 SNR。我们还检查了银河混乱噪声对 SNR 的影响，并发现由于此类噪声，SNR 出现了下降。对于非奇异 BH，随着非奇异参数的增加，出现更大质量 BH 的倾角。非奇异 BH 在 SNR 的峰和谷上的印记意味着当 BH 足够大时，非奇异 BH 很可能与标准 Schwarzschild BH 区分开来。预计 LISA 或 Taiji 更有可能实现对非奇异 BH 的检测。