Exploring nonsingular black holes in gravitational perturbations

Abstract

We calculate gravitational perturbation quasinormal modes (QNMs) of nonsingular 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 nonsingular BHs in single-mode gravitational waveform detections in the Laser Interferometer Space Antenna (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 nonsingular parameters leads to higher SNR for more massive nonsingular 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 nonsingular BHs, with the increase of the nonsingular parameters, the dip emerges for more massive BHs. It suggests a wider range of mass of nonsingular black holes whose SNR will not be lowered by galactic noise, which implies the SNR for the super massive black holes centered at our galaxy is less likely to be influenced by galactic noise in nonsingular black hole models than a singular case in general relativity. We conduct a Fisher analysis, which suggests that the nonsingular black holes parameters can be detected accurately with measurement errors as small as $\ensuremath{\sim}{10}^{\ensuremath{-}4}--{10}^{\ensuremath{-}5}$. The detections of nonsingular BHs are expected to be realized more likely by LISA or TaiJi.